Negative-feedback amplifier

2877: 1725: 3561: 2467: 20: 4826: 4289:), directly decides the effect of feedback upon the input and output resistances of the amplifier. In the case of a shunt connection, the input impedance is reduced by this factor; and in the case of series connection, the impedance is multiplied by this factor. However, the impedance that is modified by feedback is the impedance of the amplifier in Figure 5 with the feedback turned off, and does include the modifications to impedance caused by the resistors of the feedback network. 1628: 4953:) for determining input and output impedance might not work. This situation is awkward, because a failure to make a two-port may reflect a real problem (it just is not possible), or reflect a lack of imagination (for example, just did not think of splitting the emitter node in two). As a consequence, when the port conditions are in doubt, at least two approaches are possible to establish whether improvement factors are accurate: either simulate an example using 2546: 2329: 1096: 1238: 3572:, but interjecting a negative feedback amplifier can increase the apparent load seen by the source, and reduce the apparent driver impedance seen by the load, avoiding signal attenuation by voltage division. This advantage is not restricted to voltage amplifiers, but analogous improvements in matching can be arranged for current amplifiers, transconductance amplifiers and transresistance amplifiers. 3284: 236:, he recorded the diagram found in Figure 1 and the equations derived below. On August 8, 1928, Black submitted his invention to the U. S. Patent Office, which took more than 9 years to issue the patent. Black later wrote: "One reason for the delay was that the concept was so contrary to established beliefs that the Patent Office initially did not believe it would work." 1623:{\displaystyle {\begin{aligned}A_{\text{FB}}(f)&={\frac {A_{\text{OL}}}{1+\beta A_{\text{OL}}}}\\&={\frac {A_{0}/(1+jf/f_{\text{C}})}{1+\beta A_{0}/(1+jf/f_{\text{C}})}}\\&={\frac {A_{0}}{1+jf/f_{\text{C}}+\beta A_{0}}}\\&={\frac {A_{0}}{(1+\beta A_{0})\left(1+j{\frac {f}{(1+\beta A_{0})f_{\text{C}}}}\right)}}.\end{aligned}}} 2362:

These connections are usually referred to as series or shunt (parallel) connections. In the diagram, the left column shows shunt inputs; the right column shows series inputs. The top row shows series outputs; the bottom row shows shunt outputs. The various combinations of connections and two-ports are listed in the table below.

7637:

Of course this experiment gives the impression that more feedback is worse. You have to get past that bump. Hardly anybody who has ever tried it like this has actually heard the inevitable (and frankly magical) improvement that happens once you do get beyond, say 20 or 30dB. From there on you get an

3082: 2968:

Figure 3 indicates the output node, but not the choice of output variable. A useful choice is the short-circuit current output of the amplifier (leading to the short-circuit current gain). Because this variable leads simply to any of the other choices (for example, load voltage or load current), the

2361:

Negative-feedback amplifiers of any type can be implemented using combinations of two-port networks. There are four types of two-port network, and the type of amplifier desired dictates the choice of two-ports and the selection of one of the four different connection topologies shown in the diagram.

2454:

For example, for a current-feedback amplifier, current from the output is sampled for feedback and combined with current at the input. Therefore, the feedback ideally is performed using an (output) current-controlled current source (CCCS), and its imperfect realization using a two-port network also

1781:

assumptions as to the unilateral or bilateral properties of the open loop and feedback subcircuits. Moreover, they are not predicated on mutually independent open loop and feedback subcircuit transfer functions, and they do not require that feedback be implemented only globally. Indeed signal flow

2358:. The objective for the feedback amplifier may be any one of the four types of amplifier and is not necessarily the same type as the open-loop amplifier, which itself may be any one of these types. So, for example, an op amp (voltage amplifier) can be arranged to make a current amplifier instead. 1708:

blocks (that is, with their own individually determined transfer functions), a simple example of what often is called "circuit partitioning", which refers in this instance to the division into a forward amplification block and a feedback block. In practical amplifiers, the information flow is not

4458:

The impedance seen by the load needs further discussion. The load in Figure 5 is connected to the collector of the output transistor, and therefore is separated from the body of the amplifier by the infinite impedance of the output current source. Therefore, feedback has no effect on the output

7551:

most of the harmonic distortion has been masked, however, a couple of the high order harmonics were far enough away in frequency and loud enough to be heard. So in order to determine the audibility of harmonic distortion, we have to know how much masking is done by different tones at different

7461:

The equivalence of the main amplifier block to a two-port network guarantees that performance factors work, but without that equivalence they may work anyway. For example, in some cases the circuit can be shown equivalent to another circuit that is a two port, by "cooking up" different circuit

4937:

Of course, the way the ground leads are connected makes no difference to the amplifier (they are all one node), but it makes a difference to the port conditions. This artificiality is a weakness of this approach: the port conditions are needed to justify the method, but the circuit really is

7605:

Here we see that as low feedback figures are applied to a single gain stage the 2nd harmonic declines linearly with feedback, but increased amounts of higher order harmonics are created. As feedback increases above about 15 dB or so, all these forms of distortion in proportion to increased

6949: 4813: 1675:

When the close-loop gain has several poles, rather than the single pole of the above example, feedback can result in complex poles (real and imaginary parts). In a two-pole case, the result is peaking in the frequency response of the feedback amplifier near its corner frequency and

2607:= 0. which makes the CCCS on the left side an open circuit. The algebra in these two cases is simple, much easier than solving for all variables at once. The choice of g-parameters that make the two-port and the L-section behave the same way are shown in the table below. 4672: 3531: 769: 4222: 1782:

techniques do not even require explicit identification of the open loop and feedback subcircuits. Signal flow thus removes the detriments pervasive of conventional feedback network analyses but additionally, it proves to be computationally efficient as well."

4861:

Is the main amplifier block also a two-port? The main amplifier is shown in the upper shaded box. The ground connections are labeled. Figure 7 shows the interesting fact that the main amplifier does not satisfy the port conditions at its input and output

2542:. That is, the monitored output signal is really the voltage at the collector of the input transistor. That view is legitimate, but then the voltage follower stage becomes part of the feedback network. That makes analysis of feedback more complicated. 3887: 6268:

After applying moderate amounts of negative feedback (10–15 dB), the low-order harmonics are reduced, but higher-order harmonics are introduced. Since these are not masked as well, the distortion becomes audibly worse, even though the overall

3406: 6284:

harmonics are reduced, returning the distortion to inaudibility, and then improving it beyond the original zero-feedback stage (provided the system is strictly stable). So the problem is not negative feedback, but insufficient amounts of it.

4425: 4044: 2267: 795:

is set by the feedback constant β, and hence set by the feedback network, usually a simple reproducible network, thus making linearizing and stabilizing the amplification characteristics straightforward. If there are conditions where β

658: 295:

to (a) give frequency-dependent closed-loop gain as in equalization/tone-control circuits or (b) construct oscillators. The gain of the amplifier with feedback is derived below in the case of a voltage amplifier with voltage feedback.

3279:{\displaystyle A_{\mathrm {OL} }={\frac {\beta i_{\mathrm {B} }}{i_{\mathrm {S} }}}=g_{m}R_{\mathrm {C} }\left({\frac {\beta }{\beta +1}}\right)\left({\frac {R_{1}}{R_{22}+{\frac {r_{\pi 2}+R_{\mathrm {C} }}{\beta +1}}}}\right)\ .} 568: 5834: 5596: 5358: 5124: 477: 7355:

If the feedforward is included, its effect is to cause a modification of the open-loop gain, normally so small compared to the open-loop gain itself that it can be dropped. Notice also that the main amplifier block is

133:) and can provide other benefits. If not designed correctly, amplifiers with negative feedback can under some circumstances become unstable due to the feedback becoming positive, resulting in unwanted behavior such as 3714: 4698: 2578:

and find the only one with a CCCS is the g-parameter two-port, shown in Figure 4. The next task is to select the g-parameters so that the two-port of Figure 4 is electrically equivalent to the L-section made up of

366: 1194: 951: 2332:

Various topologies for a negative-feedback amplifier using two-ports. Top left: current-amplifier topology; top right: transconductance; bottom left: transresistance; bottom right: voltage-amplifier topology.

1103:

Feedback can be used to extend the bandwidth of an amplifier at the cost of lowering the amplifier gain. Figure 2 shows such a comparison. The figure is understood as follows. Without feedback the so-called

4496:

The gain derived above is the current gain at the collector of the output transistor. To relate this gain to the gain when voltage is the output of the amplifier, notice that the output voltage at the load

4933:

of the input transistor into a base-side and a collector-side – a physically impossible thing to do, but electrically the circuit sees all the ground connections as one node, so this fiction is permitted.

2346:

is the approach most often presented in textbooks and is presented here. It retains a two-block circuit partition of the amplifier, but allows the blocks to be bilateral. Some drawbacks of this method are

7573:

Masking is a principle concept in the perception of distortion, as distortion products will only contribute to the percept of distortion if they are not masked by the primary stimulus or other distortion

2027: 2752: 2485:. The aim is to analyze this circuit to find three items: the gain, the output impedance looking into the amplifier from the load, and the input impedance looking into the amplifier from the source. 2990:= 0. The idea is to find how much the amplifier gain is changed because of the resistors in the feedback network by themselves, with the feedback turned off. This calculation is pretty easy because 2813: 2521:

that is subtracted from the current entering the base of the input transistor. That is, the input side of the two-port is a dependent current source controlled by the voltage at the top of resistor

4572: 2104: 6828: 3412: 2688: 1243: 7243: 5954: 5894: 5418: 5244: 676: 4099: 3583:

Figure 6 shows an equivalent circuit for finding the input resistance of a feedback voltage amplifier (left) and for a feedback current amplifier (right). These arrangements are typical

1085: 1044: 402: 6253:

configuration have primarily low-order distortion, such as the 2nd and 3rd harmonics. In audio systems, these can be minimally audible because musical signals are typically already a

3575:

To explain these effects of feedback upon impedances, first a digression on how two-port theory approaches resistance determination, and then its application to the amplifier at hand.

2868: 5716: 5656: 5478: 5184: 4976:. That choice may be advisable if small-signal device models are complex, or are not available (for example, the devices are known only numerically, perhaps from measurement or from 3604:

travelling over the loop (but in respect to ground, the polarities are the same). As a result, the effective voltage across and the current through the amplifier input resistance

6858: 4480:

of the output transistor (instead of its collector), which is series connected to the feedback network, feedback would increase this resistance by the improvement factor ( 1 + β

3768: 4887:. To satisfy the port condition for the main amplifier, all three components must be returned to the input side of the main amplifier, which means all the ground leads labeled 3317: 50:) and reduces sensitivity to parameter variations due to manufacturing or environment. Because of these advantages, many amplifiers and control systems use negative feedback. 6391: 7509: 2354:

Electronic amplifiers use current or voltage as input and output, so four types of amplifier are possible (any of two possible inputs with any of two possible outputs). See

2151: 1761:

In these more general cases, the amplifier is analyzed more directly without the partitioning into blocks like those in the diagram, using instead some analysis based upon

1633:

The last expression shows that the feedback amplifier still has a single-time-constant behavior, but the corner frequency is now increased by the improvement factor (1 + β

894: 3568:

Feedback is used to better match signal sources to their loads. For example, a direct connection of a voltage source to a resistive load may result in signal loss due to

283:

in general may be a function of both frequency and voltage; the feedback parameter β is determined by the feedback network that is connected around the amplifier. For an

4335: 1713:

to allow inclusion of bilateral information transfer. Casting an amplifier into this form is a non-trivial task, however, especially when the feedback involved is not

1003: 803:= −1, the amplifier has infinite amplification – it has become an oscillator, and the system is unstable. The stability characteristics of the gain feedback product β 3955: 6239: 6041: 2162: 973: 2574:. The variable controlling the feedback is the emitter current, so the feedback is a current-controlled current source (CCCS). We search through the four available 579: 287:, two resistors forming a voltage divider may be used for the feedback network to set β between 0 and 1. This network may be modified using reactive elements like 220:

independently invented the negative-feedback amplifier while he was a passenger on the Lackawanna Ferry (from Hoboken Terminal to Manhattan) on his way to work at

6206: 6186: 6166: 6146: 6126: 6106: 6086: 6061: 6021: 6001: 5981: 6647: 495: 4269:

A broader conclusion, independent of the quantitative details, is that feedback can be used to increase or to decrease the input and output impedance.

4266:

current entering and leaving the input terminals, and likewise, the same current that leaves one output terminal must enter the other output terminal.

2880:

Figure 5: Small-signal circuit with two-port for feedback network; upper shaded box: main amplifier; lower shaded box: feedback two-port replacing the

1786:

Following up on this suggestion, a signal-flow graph for a negative-feedback amplifier is shown in the figure, which is patterned after one by D'Amico

7263: 5737: 5499: 5261: 5027: 204:)—that exposes these impedances to variations in the open-loop gain, for example, due to parameter variations or nonlinearity of the open-loop gain. 7032: 4840:

Figure 7 shows the small-signal schematic with the main amplifier and the feedback two-port in shaded boxes. The feedback two-port satisfies the

7496:

Great care must be exercised in applying two-port theory to ensure that the amplifier feedback networks can actually be represented as two-ports

6544: 4808:{\displaystyle {\frac {i_{\mathrm {L} }}{i_{\mathrm {S} }}}=A_{\mathrm {FB} }{\frac {R_{\mathrm {C2} }}{R_{\mathrm {C2} }+R_{\mathrm {L} }}}\ .} 4969: 7650: 3634: 417: 224:(located in Manhattan instead of New Jersey in 1927) on August 2, 1927 (US Patent 2,102,671, issued in 1937). Black was working on reducing 1114: 901: 46:

opposes the original signal. The applied negative feedback can improve its performance (gain stability, linearity, frequency response,

7535: 312: 7226: 1228:= 10 V/V. The figure shows that the gain is flat out to the corner frequency and then drops. When feedback is present, the so-called 4262:. However, the results do depend upon the main amplifier having a representation as a two-port – that is, the results depend on the 2272:

To employ this formula, one has to identify a critical controlled source for the particular amplifier circuit in hand. For example,

4929:. That forces the ground currents to divide between the input and output sides as planned. Notice that this connection arrangement 4866:

the ground connections are chosen to make that happen. For example, on the input side, the current entering the main amplifier is

1956: 7473: 4091:. Substituting this result in the above equation and solving for the input resistance of the feedback amplifier, the result is: 3760:. Substituting this result in the above equation and solving for the input resistance of the feedback amplifier, the result is: 2456: 7683: 4452: 3309:) is neglected. That makes the circuit of Figure 5 resemble the block diagram of Figure 1, and the gain with feedback is then: 1777:"In contrast to block diagram and two-port approaches to the feedback network analysis problem, signal flow methods mandate no 4667:{\displaystyle {\frac {v_{\mathrm {L} }}{i_{\mathrm {S} }}}=A_{\mathrm {FB} }(R_{\mathrm {C2} }\parallel R_{\mathrm {L} })\ .} 2696: 7398: 6476: 2760: 4945:

of ground conditions leads to the port conditions, the circuit might not behave the same way. The improvement factors (1 + β

3526:{\displaystyle A_{\mathrm {FB} }={\frac {A_{\mathrm {OL} }}{1+{\frac {R_{2}}{R_{2}+R_{\mathrm {f} }}}A_{\mathrm {OL} }}}\ ,} 2460: 2342:, some form of signal-flow analysis is the most general way to treat the negative-feedback amplifier, representation as two 4957:

and compare results with use of an improvement factor, or calculate the impedance using a test source and compare results.

2560:

is set by the emitter current of the output transistor. That view leads to an entirely passive feedback network made up of

2033: 764:{\displaystyle A_{\text{FB}}={\frac {V_{\text{out}}}{V_{\text{in}}}}={\frac {A_{\text{OL}}}{1+\beta \cdot A_{\text{OL}}}}.} 6920: 814:(a polar plot of the gain/phase shift as a parametric function of frequency). A simpler, but less general technique, uses 6277:

manufacturers to market their amplifiers as "zero feedback" (even when they use local feedback to linearize each stage).

2642: 5900: 5840: 5364: 5190: 6405: 6350: 4217:{\displaystyle R_{\mathrm {in} }(fb)={\frac {V_{x}}{I_{x}}}={\frac {R_{\mathrm {in} }}{\left(1+\beta A_{i}\right)}}\ .} 1688:. In the case of more than two poles, the feedback amplifier can become unstable and oscillate. See the discussion of 7519: 7318: 7291: 7202: 7130: 7097: 7064: 6959: 6903: 6870: 6838: 6808: 6779: 6713: 6680: 6630: 6592: 6486: 6459: 6432: 6341: 6273:

may go down. This has led to a persistent myth that negative feedback is detrimental in audio amplifiers, leading

6654: 6371: 3944: 1721:(that is, feedback within the network, involving nodes that do not coincide with input and/or output terminals). 1099:

Figure 2: Gain vs. frequency for a single-pole amplifier with and without feedback; corner frequencies are labeled

7340: 6345: 4231:

A parallel feedback connection at the input (output) decreases the input (output) resistance by a factor ( 1 + β

1051: 6981: 1013: 374: 53:

An idealized negative-feedback amplifier as shown in the diagram is a system of three elements (see Figure 1):

7772: 7489: 3896:

A series feedback connection at the input (output) increases the input (output) resistance by a factor ( 1 + β

2821: 5662: 5602: 5424: 5130: 4440:: the feedback two-port is in parallel with the signal source at the input side of the amplifier. A reminder: 2593:. That selection is an algebraic procedure made most simply by looking at two individual cases: the case with 7377:) requires care, particularly for the case of output impedance using series feedback. See Jaeger, note below. 3619: 2459:. Here the two-port method used in most textbooks is presented, using the circuit treated in the article on 1848:, model a controlled generator, or the relation between voltage and current across two nodes of the circuit. 7767: 7258: 6309: 4960:

A more practical choice is to drop the two-port approach altogether, and use various alternatives based on

4915:. Then, at the bottom of the schematic, underneath the feedback two-port and outside the amplifier blocks, 3882:{\displaystyle R_{\mathrm {in} }(fb)={\frac {V_{x}}{I_{x}}}=\left(1+\beta A_{v}\right)R_{\mathrm {in} }\ .} 2907:

The next step is to draw the small-signal schematic for the amplifier with the two-port in place using the

6620: 3929:. As a result, the total current flowing through the circuit input (not only through the input resistance 3401:{\displaystyle A_{\mathrm {FB} }={\frac {A_{\mathrm {OL} }}{1+{\beta }_{\mathrm {FB} }A_{\mathrm {OL} }}}} 276:β, which governs how much of the output signal is applied to the input (see Figure 1). The open-loop gain 3623: 1932:

Using this graph, these authors derive the generalized gain expression in terms of the control parameter

1917:

gives the relation between the independent and the controlled inner variables setting control parameter,

138: 6979: 6753: 6729: 6503: 1642: 7565: 1640:), and the gain at zero frequency has dropped by exactly the same factor. This behavior is called the 6555: 6270: 7737: 7001: 216:

Paul Voigt patented a negative feedback amplifier in January 1924, though his theory lacked detail.

7658: 3922:

of the feedback network is applied in parallel and with an opposite direction to the input current

2110: 872: 411:

applied to the other subtractor input. The result of subtraction applied to the amplifier input is

404:

of the output to one of the subtractor inputs so that it subtracts from the circuit input voltage

82: 4229:

The general conclusion from this example and a similar example for the output resistance case is:

3894:

The general conclusion from this example and a similar example for the output resistance case is:

1689: 815: 7081: 6254: 4420:{\displaystyle R_{\mathrm {in} }={\frac {R_{1}}{1+{\beta }_{\mathrm {FB} }A_{\mathrm {OL} }}}\ ,} 7313:(Fifth ed.). New York: Oxford. Example 8.4, pp. 825–829 and PSpice simulation pp. 855–859. 6815:

dividing a circuit into smaller parts ......the number of connections between parts is minimized

4039:{\displaystyle I_{x}={\frac {V_{\mathrm {in} }}{R_{\mathrm {in} }}}+\beta i_{\mathrm {out} }\ .} 3936:) increases and the voltage across it decreases so that the circuit input resistance decreases ( 3597:

of the feedback network is applied in series and with an opposite polarity to the input voltage

7053:

Ultra Low Power Bioelectronics: Fundamentals, Biomedical Applications, and Bio-Inspired Systems

6996: 6326: 6318:(emitter follower) is dedicated to the basic transistor amplifying stage with negative feedback 2876: 2600:= 0, which makes the VCVS on the right side of the two-port a short-circuit; and the case with 2262:{\displaystyle {\frac {x_{\text{O}}}{x_{\text{S}}}}=a_{11}+{\frac {a_{12}a_{21}P}{1-Pa_{22}}}.} 244:

Using the model of two unilateral blocks, several consequences of feedback are simply derived.

7590: 7194: 7048: 6887: 6796: 980: 7357: 7114: 7026: 6705: 6698: 6337: 6321: 6299: 6294: 4973: 4255: 1770: 653:{\displaystyle V_{\text{out}}(1+\beta \cdot A_{\text{OL}})=V_{\text{in}}\cdot A_{\text{OL}}.} 284: 7147: 6334:

is a powerful tool for determining the input/output impedances of negative feedback circuits

6214: 6026: 3584: 958: 207:

Changes the composition of the distortion (increasing audibility) if insufficiently applied.

7221: 7159: 6258: 1860:

is the transfer function between the input and the output setting the control parameter,

1724: 217: 160: 7622: 6608:

Black, Harold (December 1977). "Inventing the negative feedback amplifier". IEEE Spectrum.

4679:

Similarly, if the output of the amplifier is taken to be the current in the load resistor

8: 4251: 3296:

In the classical approach to feedback, the feedforward represented by the VCVS (that is,

7623:"Negative feedback in audio amplifiers: Why there is no such thing as too much (Part 2)" 7163: 4277:

These resistance results now are applied to the amplifier of Figure 3 and Figure 5. The

81:, which senses the output signal and possibly transforms it in some way (for example by 7014: 6980:

Arnaldo D’Amico, Christian Falconi, Gianluca Giustolisi, Gaetano Palumbo (April 2007).

6522: 6191: 6171: 6151: 6131: 6111: 6091: 6071: 6046: 6006: 5986: 5966: 4837:

Some drawbacks of the two two-port approach follow, intended for the attentive reader.

1681: 563:{\displaystyle V_{\text{out}}=A_{\text{OL}}(V_{\text{in}}-\beta \cdot V_{\text{out}}).} 126: 118: 62: 3560: 7515: 7485: 7394: 7314: 7287: 7198: 7187: 7126: 7093: 7060: 6955: 6899: 6866: 6834: 6804: 6775: 6741:β is the feedback loop attenuation, or feedback factor ... noise gain is equal to 1/β 6709: 6676: 6626: 6588: 6482: 6455: 6428: 6401: 4965: 4961: 1892:

represents the transfer function between the source variable and the inner variable,

1762: 1729: 1677: 221: 146: 122: 86: 43: 7694: 7018: 4873:. This current is divided three ways: to the feedback network, to the bias resistor 7167: 7006: 6518: 6315: 5485: 4988:

Summarizing the two-port analysis of feedback, one can get this table of formulas.

4841: 4687: 4259: 3569: 2575: 2532: 2494: 2455:

must incorporate a CCCS, that is, the appropriate choice for feedback network is a

2343: 2277: 1710: 1211: 1207: 7462:

parameters that are functions of the original ones. There is no end to creativity!

2535:, transmitting the voltage at the collector of the input transistor to the top of 2320:= 0 (no feedforward), we regain the simple result with two unidirectional blocks. 7267: 7230: 5723: 2908: 5829:{\displaystyle A_{zf}={\frac {V_{o}}{I_{i}}}={\frac {A_{z}}{1+\beta _{g}A_{z}}}} 5591:{\displaystyle A_{gf}={\frac {I_{o}}{V_{i}}}={\frac {A_{g}}{1+\beta _{z}A_{g}}}} 5353:{\displaystyle A_{if}={\frac {I_{o}}{I_{i}}}={\frac {A_{i}}{1+\beta _{i}A_{i}}}} 5119:{\displaystyle A_{vf}={\frac {V_{o}}{V_{i}}}={\frac {A_{v}}{1+\beta _{v}A_{v}}}} 96:(the circle in the figure), which combines the input and the transformed output. 6931: 6892:

Analog Integrated Circuits for Communication: Principles, Simulation and Design

6736: 6361: 6331: 6250: 3552:

is introduced for the feedback factor to distinguish it from the transistor β.

1808:

represent the input and output signals, moreover, two other generic variables,

866: 7010: 6845:

In real cases, unfortunately, blocks...cannot be assumed to be unidirectional.

4825: 4292:

Therefore, the input impedance seen by the source with feedback turned off is

2466: 7761: 7540:

Audioholics Home Theater, HDTV, Receivers, Speakers, Blu-ray Reviews and News

7388: 1685: 179: 142: 47: 19: 3611:

decrease so that the circuit input resistance increases (one might say that

1108:

gain in this example has a single-time-constant frequency response given by

306:

is applied directly to the amplifier input. The according output voltage is

232:

amplifiers used for telephone transmission. On a blank space in his copy of

7566:"Perception & Thresholds of Nonlinear Distortion using Complex Signals" 7279: 6366: 6356: 4505: 2355: 1766: 811: 663:

Then the gain of the amplifier with feedback, called the closed-loop gain,

166:

Can increase or decrease output impedance (depending on type of feedback).

7308: 6769: 262:, is derived in terms of the gain of the amplifier without feedback, the 134: 106: 36: 7393:(Third ed.). McGraw-Hill Professional. Example 17.3 pp. 1092–1096. 3709:{\displaystyle V_{x}=I_{x}R_{\mathrm {in} }+\beta v_{\mathrm {out} }\ ,} 3564:

Figure 6: Circuit set-up for finding feedback amplifier input resistance

1871:

is the transfer function between the output and the controlled variable

472:{\displaystyle V'_{\text{in}}=V_{\text{in}}-\beta \cdot V_{\text{out}}.} 6274: 3943:

apparently decreases). Its new value can be calculated by applying the

2545: 1095: 225: 169:

Reduces total distortion if sufficiently applied (increases linearity).

130: 7281: 6582: 6571:

Currently on display at Bell Laboratories in Mountainside, New Jersey.

6449: 6422: 2488: 2328: 1709:

unidirectional as shown here. Frequently these blocks are taken to be

7171: 6304: 2276:

could be the control parameter of one of the controlled sources in a

1007: 834: 288: 105:

Fundamentally, all electronic devices that provide power gain (e.g.,

39: 1189:{\displaystyle A_{\text{OL}}(f)={\frac {A_{0}}{1+jf/f_{\text{C}}}},} 946:{\displaystyle {\frac {A_{\text{OL}}}{1+\beta \cdot A_{\text{OL}}}}} 6885: 6396:(Paperback ed.). Prentice-Hall of India Pvt Ltd. pp. 191 4250:

These conclusions can be generalized to treat cases with arbitrary

3618:

apparently increases). Its new value can be calculated by applying

2478:

Figure 3 shows a two-transistor amplifier with a feedback resistor

292: 229: 7738:"The 'F' word, or why there is no such thing as too much feedback" 6312:

considers the basic op-amp amplifying stage with negative feedback

6280:

However, as the amount of negative feedback is increased further,

3915:

On the other hand, for the current amplifier, the output current β

1732:

for the negative-feedback amplifier based upon a control variable

6447: 6262: 371:

Suppose now that an attenuating feedback loop applies a fraction

361:{\displaystyle V_{\text{out}}=A_{\text{OL}}\cdot V'_{\text{in}}.} 200:) become sensitive to the gain of an amplifier without feedback ( 7507: 7471: 7112: 6947: 6826: 6774:. New York; Berlin: Springer. pp. §0513-§0533, p. 155–165. 6420: 4938:

unaffected by how currents are traded among ground connections.

2911:

for the transistors. Figure 5 shows the schematic with notation

42:

that subtracts a fraction of its output from its input, so that

1232:

gain, as shown in the formula of the previous section, becomes

788:≈ 1 / β, and the effective amplification (or closed-loop gain) 7413:

That is, the impedance found by turning off the signal source

6730:"MT-044 Op Amp Open Loop Gain and Open Loop Gain Nonlinearity" 196:

Input and output impedances of a negative-feedback amplifier (

6989:

IEEE Transactions on Circuits and Systems – II Express Briefs

6353:

shows the most typical op-amp circuits with negative feedback

4977: 4954: 7480:(2nd ed.). McGraw=Hill Higher Education. pp. 1409 4476:

If instead we wanted to find the impedance presented at the

2348: 2022:{\displaystyle x_{\text{O}}=a_{11}x_{\text{S}}+a_{12}x_{j},} 1819:

linked together through the control (or critical) parameter

252:

Below, the voltage gain of the amplifier with feedback, the

7474:"§18.7: Common errors in applying two-port feedback theory" 6982:"Resistance of Feedback Amplifiers: A novel representation" 6918: 2493:

The first step is replacement of the feedback network by a

7280:

P. R. Gray; P. J. Hurst; S. H. Lewis; R. G. Meyer (2001).

6257:, and the low-order distortion products are hidden by the 4820: 3590:

In the case of the voltage amplifier, the output voltage β

2531:

One might say the second stage of the amplifier is just a

6393:

Basic Electronics: Devices, Circuits, and IT fundamentals

3578: 114: 110: 7536:"Nonlinear Distortion and Perception at Low Frequencies" 6454:. Boston/Dordrecht/London: Kluwer Academic. p. 64. 4851:

enters and leaves the port, and likewise at the output,

4455:, as modified by the resistors of the feedback network. 2747:{\displaystyle -{\frac {R_{2}}{R_{2}+R_{\mathrm {f} }}}} 1790:. Following these authors, the notation is as follows: 1773:. Commenting upon the signal-flow approach, Choma says: 832:

appears commonly in feedback analysis and is called the

7386: 4901:. Likewise, on the output side, all ground connections 4829:

Figure 7: Amplifier with ground connections labeled by

4327:, and with the feedback turned on (but no feedforward) 4272: 2808:{\displaystyle {\frac {R_{2}}{R_{2}+R_{\mathrm {f} }}}} 1700:

A principal idealization behind the formulation of the

149:

is used to study the stability of feedback amplifiers.

7306: 7286:(Fourth ed.). New York: Wiley. pp. 586–587. 7115:"§3.3 The Rosenstark Method and §3.4 The Choma Method" 6894:. Springer Science & Business Media. pp. 105 2553:

An alternative view is that the voltage at the top of

845:) also appears commonly and is variously named as the 7514:. Springer Science & Business Media. p. 66. 7121:. Springer Science & Business Media. pp. 69 6954:. Springer Science & Business Media. p. 66. 6622:

Electronic Circuits: Analysis, Simulation, and Design

6217: 6194: 6174: 6154: 6134: 6114: 6094: 6074: 6049: 6029: 6009: 5989: 5969: 5903: 5843: 5740: 5665: 5605: 5502: 5427: 5367: 5264: 5193: 5133: 5030: 4833:. The feedback network satisfies the port conditions. 4701: 4575: 4338: 4102: 3958: 3771: 3637: 3415: 3320: 3085: 2824: 2763: 2699: 2645: 2165: 2113: 2099:{\displaystyle x_{i}=a_{21}x_{\text{S}}+a_{22}x_{j},} 2036: 1959: 1241: 1117: 1054: 1016: 983: 961: 904: 875: 679: 582: 498: 420: 377: 315: 1717:(that is directly from the output to the input) but 4880:and to the base resistance of the input transistor 4690:determines the load current, and the gain is then: 2683:{\displaystyle {\frac {1}{R_{\mathrm {f} }+R_{2}}}} 2489:

Replacement of the feedback network with a two-port

7564:de Santis, Eric Mario; Henin, Simon (2007-06-07). 7420:= 0, inserting a test current in the emitter lead 7186: 6794: 6767: 6704:(2 ed.). Cambridge University Press. p. 6697: 6233: 6200: 6180: 6160: 6140: 6120: 6100: 6080: 6055: 6035: 6015: 5995: 5975: 5949:{\displaystyle {\frac {R_{o}}{1+\beta _{g}A_{z}}}} 5948: 5889:{\displaystyle {\frac {R_{i}}{1+\beta _{g}A_{z}}}} 5888: 5828: 5710: 5650: 5590: 5472: 5413:{\displaystyle {\frac {R_{i}}{1+\beta _{i}A_{i}}}} 5412: 5352: 5239:{\displaystyle {\frac {R_{o}}{1+\beta _{v}A_{v}}}} 5238: 5178: 5118: 4807: 4666: 4419: 4216: 4038: 3881: 3708: 3525: 3400: 3278: 2862: 2807: 2746: 2682: 2261: 2145: 2098: 2021: 1906:is set to zero (i.e., when the control parameter, 1622: 1188: 1079: 1038: 997: 967: 945: 888: 763: 652: 562: 471: 396: 360: 190:May lead to instability if not designed carefully. 7670:Dreadnaught III uses no global negative feedback. 7638:unambiguous net improvement that goes on forever. 7283:Analysis and Design of Analog Integrated Circuits 6675:(6 ed.). New York: Focal Press. p. 54. 6448:Palumbo, Gaetano & Salvatore Pennisi (2002). 7759: 7184: 7046: 6948:Gaetano Palumbo & Salvatore Pennisi (2002). 6545:"U.S. Patent 2,102,671: Wave Translation System" 6421:Kuo, Benjamin C. & Farid Golnaraghi (2003). 4491: 2976:is found. The feedback is turned off by setting 2323: 1936:that defines the controlled source relationship 7193:(International ed.). McGraw-Hill. p. 6580: 6517:(1). American Telephone & Telegraph: 1–18. 3622:(for voltages) or the basic circuit laws. Thus 3555: 7681: 7563: 7086:Circuit Analysis and Feedback Amplifier Theory 6886:Donald O. Pederson; Kartikeya Mayaram (2007). 4983: 3947:(for currents) or the basic Kirchhoff's laws: 2156:Combining these results, the gain is given by 7735: 7427:, finding the voltage across the test source 7345:(4th ed.). pp. 851–946. Chapter 12. 7342:Neamen Electronic Circuit Analysis And Design 6863:Feedback, Nonlinear, and Distributed Circuits 6696:Horowitz, Paul; Hill, Winfield (1989-07-28). 6607: 4908:must be connected and also ground connection 2497:. Just what components go into the two-port? 7145: 7079: 7031:: CS1 maint: multiple names: authors list ( 6856: 6755:Analog circuit design: lectures on stability 6695: 6389: 4550:is found by multiplying the current gain by 3067:. The result for the open-loop current gain 2280:, as shown for a particular case in D'Amico 152:Feedback amplifiers share these properties: 7651:"Theta Digital – Dreadnaught III Amplifier" 7508:Gaetano Palumbo; Salvatore Pennisi (2002). 7472:Richard C Jaeger; Travis N Blalock (2004). 7273: 7148:"Signal flow analysis of feedback networks" 7113:Gaetano Palumbo; Salvatore Pennisi (2002). 7055:. Cambridge University Press. pp. 240 6827:Gaetano Palumbo; Salvatore Pennisi (2002). 4894:must be connected, as well as emitter lead 2969:short-circuit current gain is found below. 1080:{\displaystyle 1+\beta \cdot A_{\text{OL}}} 23:Figure 1: Ideal negative-feedback amplifier 7591:"Audio distortion and feedback - Passlabs" 7039: 6427:(Eighth ed.). NY: Wiley. p. 46. 4536:). Consequently, the transresistance gain 2549:Figure 4: The g-parameter feedback network 2500:On the input side of the two-port we have 1039:{\displaystyle -\beta \cdot A_{\text{OL}}} 810:are often displayed and investigated on a 397:{\displaystyle \beta \cdot V_{\text{out}}} 175:Desensitizes gain to component variations. 7369:The use of the improvement factor ( 1 + β 7152:IEEE Transactions on Circuits and Systems 7000: 6975: 6973: 6971: 6833:. Springer Science & Business Media. 2863:{\displaystyle R_{2}||R_{\mathrm {f} }\ } 2337: 1692:. For a complete discussion, see Sansen. 7501: 7185:Richard C Jaeger (1997). "Figure 18.2". 7106: 6879: 6820: 6574: 5711:{\displaystyle R_{o}(1+\beta _{z}A_{g})} 5651:{\displaystyle R_{i}(1+\beta _{z}A_{g})} 5473:{\displaystyle R_{o}(1+\beta _{i}A_{i})} 5179:{\displaystyle R_{i}(1+\beta _{v}A_{v})} 4824: 4436:is used because the input connection is 3559: 2963: 2875: 2544: 2465: 2327: 1723: 1221:= 10 Hz, and the gain at zero frequency 1094: 18: 7465: 7387:R.C. Jaeger & T.N. Blalock (2006). 7178: 7139: 6941: 6919:Scott K. Burgess & John Choma, Jr. 6912: 6888:"§5.2 Feedback for a general amplifier" 6441: 6377: 6241:means voltage feedback amplifier gain. 4821:Is the main amplifier block a two-port? 4504:is related to the collector current by 2902: 1695: 7760: 7511:Feedback Amplifiers: Theory and Design 7380: 7300: 7119:Feedback Amplifiers: Theory and Design 6968: 6951:Feedback amplifiers: theory and design 6830:Feedback Amplifiers: Theory and Design 6803:. McGraw Hill Education. p. 253. 6761: 6451:Feedback amplifiers: theory and design 6066:The subscripts and their meanings are 3579:Background on resistance determination 2507:. If the voltage at the right side of 2336:Although, as mentioned in the section 1090: 7616: 7614: 7584: 7582: 7334: 7332: 7330: 6928:Generalized feedback circuit analysis 6850: 6618: 6601: 6542: 6501: 6495: 6188:- current for gains and feedback and 5961:The variables and their meanings are 4281:that reduces the gain, namely ( 1 + β 4258:drives, arbitrary loads, and general 3291: 239: 7588: 7073: 6788: 6670: 6474: 4273:Application to the example amplifier 299:Without feedback, the input voltage 7620: 7049:"Chapter 10: Return ratio analysis" 2514:changes, it changes the current in 2284:As a different example, if we take 1830:are the weight branches. Variables 1704:is the network's division into two 860: 13: 7611: 7579: 7338: 7327: 6619:Malik, Norbert R. (January 1995). 6523:10.1002/j.1538-7305.1934.tb00652.x 6414: 6383: 6351:Operational amplifier applications 4790: 4772: 4756: 4742: 4739: 4722: 4710: 4649: 4631: 4616: 4613: 4596: 4584: 4402: 4399: 4387: 4384: 4348: 4345: 4171: 4168: 4112: 4109: 4024: 4021: 4018: 3998: 3995: 3983: 3980: 3867: 3864: 3781: 3778: 3694: 3691: 3688: 3670: 3667: 3508: 3505: 3490: 3445: 3442: 3425: 3422: 3389: 3386: 3374: 3371: 3350: 3347: 3330: 3327: 3243: 3156: 3129: 3116: 3095: 3092: 2851: 2796: 2735: 2658: 2313:= –β (negative feedback) and 1214:of the amplifier: in this example 14: 7784: 7307:A. S. Sedra; K. C. Smith (2004). 5250:Shunt-Series (current amplifier) 5016:Series-Shunt (voltage amplifier) 1823:are explicitly shown. Parameters 1736:relating two internal variables: 1670: 247: 92:a summing circuit that acts as a 6648:"The General Feedback Structure" 6504:"Stabilized Feedback Amplifiers" 4459:impedance, which remains simply 163:(depending on type of feedback). 7736:Bruno Putzeys (February 2011). 7729: 7712: 7682:Martin Colloms (January 1998). 7675: 7643: 7557: 7528: 7455: 7407: 7363: 7349: 7251: 7236: 7214: 6746: 6722: 6689: 6664: 6639: 6612: 159:Can increase or decrease input 129:for higher linearity (reducing 7478:Microelectronic circuit design 7390:Microelectronic Circuit Design 7189:Microelectronic circuit design 6645: 6565: 6536: 6468: 5705: 5676: 5645: 5616: 5467: 5438: 5173: 5144: 4655: 4622: 4127: 4118: 3796: 3787: 2841: 2836: 1899:when the controlled variable 1667:increases to 10 × 10 = 10 Hz. 1589: 1567: 1544: 1522: 1424: 1394: 1365: 1335: 1262: 1256: 1134: 1128: 618: 593: 554: 522: 1: 6502:Black, H. S. (January 1934). 6244: 4492:Load voltage and load current 4466:as seen by the load resistor 2637: 2324:Two-port analysis of feedback 2146:{\displaystyle x_{j}=Px_{i}.} 1660:(0) = 10 / 10 = 100 V/V, and 889:{\displaystyle A_{\text{OL}}} 7720:Audio power amplifier design 7684:"A Future Without Feedback?" 6673:Audio Power Amplifier Design 6671:Self, Douglas (2013-06-18). 6543:Black, Harold (1937-12-21). 6478:Op Amp Applications Handbook 3556:Input and output resistances 2356:classification of amplifiers 1690:gain margin and phase margin 16:Type of electronic amplifier 7: 7589:Pass, Nelson (2008-11-01). 7146:J. Choma, Jr (April 1990). 7088:. CRC Press. pp. 11–2 7082:"§11.2 Methods of analysis" 6921:"§6.3 Circuit partitioning" 6865:. CRC Press. pp. 1–3. 6795:Partha Pratim Sahu (2013). 6768:Willy M. C. Sansen (2006). 6288: 6249:Simple amplifiers like the 4984:Feedback amplifier formulas 3585:Miller theorem applications 3540:where the feedback factor β 1844:and the control parameter, 139:Nyquist stability criterion 100: 29:negative-feedback amplifier 10: 7789: 6859:"§1.2 Methods of analysis" 6340:presents the basic op-amp 4260:two-port feedback networks 1878:setting the input source, 1754:. Patterned after D'Amico 211: 7047:Rahul Sarpeshkar (2010). 7045:For an introduction, see 7011:10.1109/TCSII.2006.889713 6424:Automatic control systems 6208:- input for resistances. 838:. The combination (1 + β 489:in the first expression, 193:Amplifier gain decreases. 7310:Microelectronic Circuits 6771:Analog design essentials 6587:. NY: Wiley. p. 3. 6581:Waldhauer, Fred (1982). 3011:all are in parallel and 2368:Feedback amplifier type 998:{\displaystyle 1/\beta } 172:Increases the bandwidth. 7242:Zimmer T., Geoffroy D. 6342:non-inverting amplifier 4943:no possible arrangement 3624:Kirchhoff's voltage law 1643:gain–bandwidth tradeoff 1048:Desensitivity factor = 7209:editions:BZ69IvJlfW8C. 6700:The Art of Electronics 6327:Frequency compensation 6235: 6234:{\displaystyle A_{vf}} 6202: 6182: 6162: 6142: 6122: 6102: 6088:- feedback amplifier, 6082: 6057: 6037: 6036:{\displaystyle \beta } 6017: 5997: 5977: 5950: 5890: 5830: 5712: 5652: 5592: 5474: 5414: 5354: 5240: 5180: 5120: 4964:theory, including the 4834: 4809: 4668: 4421: 4218: 4040: 3883: 3710: 3565: 3527: 3402: 3280: 2899: 2864: 2809: 2748: 2684: 2550: 2475: 2333: 2263: 2147: 2100: 2023: 1910:is set to zero); term 1758: 1646:. In Figure 2, (1 + β 1624: 1190: 1100: 1081: 1040: 999: 969: 968:{\displaystyle \beta } 947: 890: 765: 654: 564: 473: 398: 362: 24: 7773:Electronic amplifiers 7080:Wai-Kai Chen (2005). 6857:Wai-Kai Chen (2009). 6390:Santiram Kal (2004). 6338:Operational amplifier 6322:Extra element theorem 6295:Asymptotic gain model 6236: 6203: 6183: 6163: 6143: 6123: 6103: 6083: 6058: 6038: 6018: 5998: 5978: 5951: 5891: 5831: 5713: 5653: 5593: 5475: 5415: 5355: 5241: 5181: 5121: 4844:: at the input port, 4828: 4810: 4669: 4422: 4219: 4041: 3884: 3711: 3563: 3528: 3403: 3281: 2964:Loaded open-loop gain 2879: 2865: 2810: 2749: 2685: 2548: 2469: 2461:asymptotic gain model 2331: 2264: 2148: 2101: 2024: 1771:asymptotic gain model 1727: 1625: 1191: 1098: 1082: 1041: 1000: 970: 948: 891: 766: 655: 565: 474: 399: 363: 285:operational amplifier 198:closed-loop amplifier 22: 7655:www.thetadigital.com 7260:Lectures on feedback 6378:References and notes 6263:human hearing system 6215: 6192: 6172: 6152: 6132: 6128:- transconductance, 6112: 6092: 6072: 6047: 6043:- feedback gain and 6027: 6007: 5987: 5967: 5901: 5841: 5738: 5663: 5603: 5500: 5425: 5365: 5262: 5191: 5131: 5028: 4699: 4573: 4336: 4100: 3956: 3769: 3635: 3413: 3318: 3083: 2903:Small-signal circuit 2884:-section made up of 2822: 2761: 2697: 2643: 2457:g-parameter two-port 2349:described at the end 2339:Signal-flow analysis 2163: 2111: 2034: 1957: 1921:and input variable, 1763:signal-flow analysis 1696:Signal-flow analysis 1239: 1115: 1052: 1014: 981: 959: 902: 873: 847:desensitivity factor 677: 580: 496: 418: 375: 313: 218:Harold Stephen Black 7768:Electronic feedback 7257:Vivek Subramanian. 7223:Feedback topologies 7164:1990ITCS...37..455C 6797:"§8.2 Partitioning" 6511:Bell System Tech. J 6475:Jung, Walt (2005). 6346:inverting amplifier 6148:- transresistance, 4996:Feedback Amplifier 4992: 4858:enters and leaves. 3945:dual Miller theorem 1767:return-ratio method 1091:Bandwidth extension 898:Closed-loop gain = 433: 354: 202:open-loop amplifier 111:bipolar transistors 7718:P. J. Baxandall, “ 7266:2008-02-29 at the 7245:Feedback amplifier 7229:2008-02-29 at the 6300:Blackman's theorem 6231: 6198: 6178: 6158: 6138: 6118: 6098: 6078: 6053: 6033: 6013: 5993: 5973: 5946: 5886: 5826: 5708: 5648: 5588: 5470: 5410: 5350: 5236: 5176: 5116: 5011:Output Resistance 5005:Transfer Function 4991: 4974:Blackman's theorem 4931:splits the emitter 4835: 4805: 4664: 4417: 4279:improvement factor 4247:= open loop gain. 4214: 4036: 3912:= open loop gain. 3879: 3706: 3566: 3523: 3398: 3292:Gain with feedback 3276: 2900: 2860: 2805: 2744: 2680: 2551: 2476: 2474:feedback amplifier 2380:Two-port feedback 2374:Output connection 2334: 2259: 2143: 2096: 2019: 1759: 1620: 1618: 1186: 1101: 1077: 1036: 995: 965: 955:Feedback factor = 943: 886: 855:improvement factor 761: 650: 560: 469: 421: 394: 358: 342: 240:Classical feedback 234:The New York Times 33:feedback amplifier 25: 7400:978-0-07-319163-8 6752:R. W. Brodersen. 6625:. Prentice Hall. 6552:www.eepatents.com 6201:{\displaystyle i} 6181:{\displaystyle i} 6161:{\displaystyle o} 6141:{\displaystyle Z} 6121:{\displaystyle g} 6101:{\displaystyle v} 6081:{\displaystyle f} 6056:{\displaystyle R} 6016:{\displaystyle V} 5996:{\displaystyle I} 5976:{\displaystyle A} 5959: 5958: 5944: 5884: 5824: 5779: 5586: 5541: 5408: 5348: 5303: 5234: 5114: 5069: 5008:Input Resistance 4966:Rosenstark method 4962:signal flow graph 4801: 4797: 4728: 4660: 4602: 4413: 4409: 4210: 4206: 4155: 4032: 4004: 3875: 3824: 3702: 3519: 3515: 3497: 3396: 3272: 3264: 3261: 3182: 3135: 2972:First the loaded 2874: 2873: 2859: 2803: 2742: 2678: 2576:two-port networks 2452: 2451: 2419:Transconductance 2371:Input connection 2254: 2188: 2185: 2175: 2067: 1990: 1967: 1730:signal-flow graph 1711:two-port networks 1611: 1603: 1599: 1497: 1477: 1428: 1421: 1362: 1305: 1301: 1281: 1253: 1181: 1177: 1125: 1074: 1033: 941: 937: 914: 883: 851:return difference 756: 752: 729: 715: 712: 702: 687: 644: 631: 615: 590: 551: 532: 519: 506: 482:Substituting for 463: 444: 428: 391: 349: 336: 323: 222:Bell Laboratories 147:Bell Laboratories 123:Negative feedback 44:negative feedback 7780: 7753: 7752: 7750: 7748: 7742: 7733: 7727: 7716: 7710: 7709: 7707: 7705: 7699: 7693:. Archived from 7688: 7679: 7673: 7672: 7667: 7666: 7657:. Archived from 7647: 7641: 7640: 7634: 7633: 7621:Putzeys, Bruno. 7618: 7609: 7608: 7602: 7601: 7586: 7577: 7576: 7570: 7561: 7555: 7554: 7552:loudness levels. 7548: 7547: 7542:. 13 August 2015 7532: 7526: 7525: 7505: 7499: 7498: 7469: 7463: 7459: 7453: 7411: 7405: 7404: 7384: 7378: 7367: 7361: 7353: 7347: 7346: 7339:Neaman, Donald. 7336: 7325: 7324: 7304: 7298: 7297: 7277: 7271: 7255: 7249: 7240: 7234: 7218: 7212: 7211: 7192: 7182: 7176: 7175: 7172:10.1109/31.52748 7143: 7137: 7136: 7110: 7104: 7103: 7077: 7071: 7070: 7043: 7037: 7036: 7030: 7022: 7004: 6986: 6977: 6966: 6965: 6945: 6939: 6938: 6936: 6930:. Archived from 6925: 6916: 6910: 6909: 6883: 6877: 6876: 6854: 6848: 6847: 6824: 6818: 6817: 6792: 6786: 6785: 6765: 6759: 6750: 6744: 6743: 6734: 6726: 6720: 6719: 6703: 6693: 6687: 6686: 6668: 6662: 6661: 6659: 6653:. Archived from 6652: 6643: 6637: 6636: 6616: 6610: 6609: 6605: 6599: 6598: 6578: 6572: 6569: 6563: 6562: 6560: 6554:. Archived from 6549: 6540: 6534: 6533: 6531: 6529: 6508: 6499: 6493: 6492: 6472: 6466: 6465: 6445: 6439: 6438: 6418: 6412: 6411: 6387: 6316:Common collector 6310:Buffer amplifier 6240: 6238: 6237: 6232: 6230: 6229: 6207: 6205: 6204: 6199: 6187: 6185: 6184: 6179: 6167: 6165: 6164: 6159: 6147: 6145: 6144: 6139: 6127: 6125: 6124: 6119: 6107: 6105: 6104: 6099: 6087: 6085: 6084: 6079: 6062: 6060: 6059: 6054: 6042: 6040: 6039: 6034: 6022: 6020: 6019: 6014: 6002: 6000: 5999: 5994: 5982: 5980: 5979: 5974: 5955: 5953: 5952: 5947: 5945: 5943: 5942: 5941: 5932: 5931: 5915: 5914: 5905: 5895: 5893: 5892: 5887: 5885: 5883: 5882: 5881: 5872: 5871: 5855: 5854: 5845: 5835: 5833: 5832: 5827: 5825: 5823: 5822: 5821: 5812: 5811: 5795: 5794: 5785: 5780: 5778: 5777: 5768: 5767: 5758: 5753: 5752: 5717: 5715: 5714: 5709: 5704: 5703: 5694: 5693: 5675: 5674: 5657: 5655: 5654: 5649: 5644: 5643: 5634: 5633: 5615: 5614: 5597: 5595: 5594: 5589: 5587: 5585: 5584: 5583: 5574: 5573: 5557: 5556: 5547: 5542: 5540: 5539: 5530: 5529: 5520: 5515: 5514: 5486:transconductance 5479: 5477: 5476: 5471: 5466: 5465: 5456: 5455: 5437: 5436: 5419: 5417: 5416: 5411: 5409: 5407: 5406: 5405: 5396: 5395: 5379: 5378: 5369: 5359: 5357: 5356: 5351: 5349: 5347: 5346: 5345: 5336: 5335: 5319: 5318: 5309: 5304: 5302: 5301: 5292: 5291: 5282: 5277: 5276: 5245: 5243: 5242: 5237: 5235: 5233: 5232: 5231: 5222: 5221: 5205: 5204: 5195: 5185: 5183: 5182: 5177: 5172: 5171: 5162: 5161: 5143: 5142: 5125: 5123: 5122: 5117: 5115: 5113: 5112: 5111: 5102: 5101: 5085: 5084: 5075: 5070: 5068: 5067: 5058: 5057: 5048: 5043: 5042: 4993: 4990: 4922:is connected to 4814: 4812: 4811: 4806: 4799: 4798: 4796: 4795: 4794: 4793: 4780: 4779: 4778: 4764: 4763: 4762: 4749: 4747: 4746: 4745: 4729: 4727: 4726: 4725: 4715: 4714: 4713: 4703: 4688:current division 4673: 4671: 4670: 4665: 4658: 4654: 4653: 4652: 4639: 4638: 4637: 4621: 4620: 4619: 4603: 4601: 4600: 4599: 4589: 4588: 4587: 4577: 4426: 4424: 4423: 4418: 4411: 4410: 4408: 4407: 4406: 4405: 4392: 4391: 4390: 4381: 4368: 4367: 4358: 4353: 4352: 4351: 4223: 4221: 4220: 4215: 4208: 4207: 4205: 4201: 4200: 4199: 4176: 4175: 4174: 4161: 4156: 4154: 4153: 4144: 4143: 4134: 4117: 4116: 4115: 4045: 4043: 4042: 4037: 4030: 4029: 4028: 4027: 4005: 4003: 4002: 4001: 3988: 3987: 3986: 3973: 3968: 3967: 3888: 3886: 3885: 3880: 3873: 3872: 3871: 3870: 3857: 3853: 3852: 3851: 3825: 3823: 3822: 3813: 3812: 3803: 3786: 3785: 3784: 3715: 3713: 3712: 3707: 3700: 3699: 3698: 3697: 3675: 3674: 3673: 3660: 3659: 3647: 3646: 3570:voltage division 3532: 3530: 3529: 3524: 3517: 3516: 3514: 3513: 3512: 3511: 3498: 3496: 3495: 3494: 3493: 3480: 3479: 3469: 3468: 3459: 3450: 3449: 3448: 3435: 3430: 3429: 3428: 3407: 3405: 3404: 3399: 3397: 3395: 3394: 3393: 3392: 3379: 3378: 3377: 3368: 3355: 3354: 3353: 3340: 3335: 3334: 3333: 3285: 3283: 3282: 3277: 3270: 3269: 3265: 3263: 3262: 3260: 3249: 3248: 3247: 3246: 3233: 3232: 3219: 3214: 3213: 3203: 3202: 3193: 3187: 3183: 3181: 3167: 3161: 3160: 3159: 3149: 3148: 3136: 3134: 3133: 3132: 3122: 3121: 3120: 3119: 3105: 3100: 3099: 3098: 2869: 2867: 2866: 2861: 2857: 2856: 2855: 2854: 2844: 2839: 2834: 2833: 2814: 2812: 2811: 2806: 2804: 2802: 2801: 2800: 2799: 2786: 2785: 2775: 2774: 2765: 2753: 2751: 2750: 2745: 2743: 2741: 2740: 2739: 2738: 2725: 2724: 2714: 2713: 2704: 2689: 2687: 2686: 2681: 2679: 2677: 2676: 2675: 2663: 2662: 2661: 2647: 2610: 2609: 2533:voltage follower 2402:Transresistance 2365: 2364: 2278:two-port network 2268: 2266: 2265: 2260: 2255: 2253: 2252: 2251: 2232: 2228: 2227: 2218: 2217: 2207: 2202: 2201: 2189: 2187: 2186: 2183: 2177: 2176: 2173: 2167: 2152: 2150: 2149: 2144: 2139: 2138: 2123: 2122: 2105: 2103: 2102: 2097: 2092: 2091: 2082: 2081: 2069: 2068: 2065: 2059: 2058: 2046: 2045: 2028: 2026: 2025: 2020: 2015: 2014: 2005: 2004: 1992: 1991: 1988: 1982: 1981: 1969: 1968: 1965: 1885:, to zero; term 1864:, to zero; term 1629: 1627: 1626: 1621: 1619: 1612: 1610: 1609: 1605: 1604: 1602: 1601: 1600: 1597: 1588: 1587: 1562: 1543: 1542: 1520: 1519: 1510: 1502: 1498: 1496: 1495: 1494: 1479: 1478: 1475: 1469: 1451: 1450: 1441: 1433: 1429: 1427: 1423: 1422: 1419: 1413: 1393: 1388: 1387: 1368: 1364: 1363: 1360: 1354: 1334: 1329: 1328: 1318: 1310: 1306: 1304: 1303: 1302: 1299: 1283: 1282: 1279: 1273: 1255: 1254: 1251: 1212:corner frequency 1195: 1193: 1192: 1187: 1182: 1180: 1179: 1178: 1175: 1169: 1151: 1150: 1141: 1127: 1126: 1123: 1086: 1084: 1083: 1078: 1076: 1075: 1072: 1045: 1043: 1042: 1037: 1035: 1034: 1031: 1004: 1002: 1001: 996: 991: 974: 972: 971: 966: 952: 950: 949: 944: 942: 940: 939: 938: 935: 916: 915: 912: 906: 895: 893: 892: 887: 885: 884: 881: 861:Summary of terms 821:The combination 770: 768: 767: 762: 757: 755: 754: 753: 750: 731: 730: 727: 721: 716: 714: 713: 710: 704: 703: 700: 694: 689: 688: 685: 659: 657: 656: 651: 646: 645: 642: 633: 632: 629: 617: 616: 613: 592: 591: 588: 569: 567: 566: 561: 553: 552: 549: 534: 533: 530: 521: 520: 517: 508: 507: 504: 478: 476: 475: 470: 465: 464: 461: 446: 445: 442: 429: 426: 403: 401: 400: 395: 393: 392: 389: 367: 365: 364: 359: 350: 347: 338: 337: 334: 325: 324: 321: 254:closed-loop gain 76:feedback network 7788: 7787: 7783: 7782: 7781: 7779: 7778: 7777: 7758: 7757: 7756: 7746: 7744: 7740: 7734: 7730: 7717: 7713: 7703: 7701: 7697: 7686: 7680: 7676: 7664: 7662: 7649: 7648: 7644: 7631: 7629: 7619: 7612: 7599: 7597: 7587: 7580: 7568: 7562: 7558: 7545: 7543: 7534: 7533: 7529: 7522: 7506: 7502: 7492: 7470: 7466: 7460: 7456: 7450: 7446: 7440: 7432: 7425: 7419: 7412: 7408: 7401: 7385: 7381: 7376: 7372: 7368: 7364: 7354: 7350: 7337: 7328: 7321: 7305: 7301: 7294: 7278: 7274: 7268:Wayback Machine 7256: 7252: 7241: 7237: 7231:Wayback Machine 7220:Ashok K. Goel. 7219: 7215: 7205: 7183: 7179: 7144: 7140: 7133: 7111: 7107: 7100: 7078: 7074: 7067: 7044: 7040: 7024: 7023: 7002:10.1.1.694.8450 6984: 6978: 6969: 6962: 6946: 6942: 6934: 6923: 6917: 6913: 6906: 6884: 6880: 6873: 6855: 6851: 6841: 6825: 6821: 6811: 6793: 6789: 6782: 6766: 6762: 6751: 6747: 6732: 6728: 6727: 6723: 6716: 6694: 6690: 6683: 6669: 6665: 6657: 6650: 6644: 6640: 6633: 6617: 6613: 6606: 6602: 6595: 6579: 6575: 6570: 6566: 6558: 6547: 6541: 6537: 6527: 6525: 6506: 6500: 6496: 6489: 6473: 6469: 6462: 6446: 6442: 6435: 6419: 6415: 6408: 6388: 6384: 6380: 6291: 6255:harmonic series 6247: 6222: 6218: 6216: 6213: 6212: 6193: 6190: 6189: 6173: 6170: 6169: 6153: 6150: 6149: 6133: 6130: 6129: 6113: 6110: 6109: 6093: 6090: 6089: 6073: 6070: 6069: 6048: 6045: 6044: 6028: 6025: 6024: 6008: 6005: 6004: 5988: 5985: 5984: 5968: 5965: 5964: 5937: 5933: 5927: 5923: 5916: 5910: 5906: 5904: 5902: 5899: 5898: 5877: 5873: 5867: 5863: 5856: 5850: 5846: 5844: 5842: 5839: 5838: 5817: 5813: 5807: 5803: 5796: 5790: 5786: 5784: 5773: 5769: 5763: 5759: 5757: 5745: 5741: 5739: 5736: 5735: 5724:transresistance 5699: 5695: 5689: 5685: 5670: 5666: 5664: 5661: 5660: 5639: 5635: 5629: 5625: 5610: 5606: 5604: 5601: 5600: 5579: 5575: 5569: 5565: 5558: 5552: 5548: 5546: 5535: 5531: 5525: 5521: 5519: 5507: 5503: 5501: 5498: 5497: 5461: 5457: 5451: 5447: 5432: 5428: 5426: 5423: 5422: 5401: 5397: 5391: 5387: 5380: 5374: 5370: 5368: 5366: 5363: 5362: 5341: 5337: 5331: 5327: 5320: 5314: 5310: 5308: 5297: 5293: 5287: 5283: 5281: 5269: 5265: 5263: 5260: 5259: 5227: 5223: 5217: 5213: 5206: 5200: 5196: 5194: 5192: 5189: 5188: 5167: 5163: 5157: 5153: 5138: 5134: 5132: 5129: 5128: 5107: 5103: 5097: 5093: 5086: 5080: 5076: 5074: 5063: 5059: 5053: 5049: 5047: 5035: 5031: 5029: 5026: 5025: 4986: 4952: 4948: 4928: 4921: 4914: 4907: 4900: 4893: 4886: 4879: 4872: 4857: 4850: 4842:port conditions 4823: 4789: 4788: 4784: 4771: 4770: 4766: 4765: 4755: 4754: 4750: 4748: 4738: 4737: 4733: 4721: 4720: 4716: 4709: 4708: 4704: 4702: 4700: 4697: 4696: 4685: 4648: 4647: 4643: 4630: 4629: 4625: 4612: 4611: 4607: 4595: 4594: 4590: 4583: 4582: 4578: 4576: 4574: 4571: 4570: 4563: 4556: 4549: 4542: 4535: 4528: 4521: 4514: 4503: 4494: 4487: 4483: 4472: 4465: 4451:open loop gain 4446: 4398: 4397: 4393: 4383: 4382: 4377: 4376: 4369: 4363: 4359: 4357: 4344: 4343: 4339: 4337: 4334: 4333: 4326: 4319: 4312: 4305: 4298: 4288: 4284: 4275: 4246: 4237: 4195: 4191: 4181: 4177: 4167: 4166: 4162: 4160: 4149: 4145: 4139: 4135: 4133: 4108: 4107: 4103: 4101: 4098: 4097: 4090: 4083: 4077: 4070: 4064: 4057: 4017: 4016: 4012: 3994: 3993: 3989: 3979: 3978: 3974: 3972: 3963: 3959: 3957: 3954: 3953: 3942: 3935: 3927: 3921: 3911: 3902: 3863: 3862: 3858: 3847: 3843: 3833: 3829: 3818: 3814: 3808: 3804: 3802: 3777: 3776: 3772: 3770: 3767: 3766: 3759: 3753: 3747: 3740: 3734: 3727: 3687: 3686: 3682: 3666: 3665: 3661: 3655: 3651: 3642: 3638: 3636: 3633: 3632: 3617: 3610: 3602: 3596: 3581: 3558: 3551: 3547: 3543: 3504: 3503: 3499: 3489: 3488: 3484: 3475: 3471: 3470: 3464: 3460: 3458: 3451: 3441: 3440: 3436: 3434: 3421: 3420: 3416: 3414: 3411: 3410: 3385: 3384: 3380: 3370: 3369: 3364: 3363: 3356: 3346: 3345: 3341: 3339: 3326: 3325: 3321: 3319: 3316: 3315: 3308: 3302: 3294: 3250: 3242: 3241: 3237: 3225: 3221: 3220: 3218: 3209: 3205: 3204: 3198: 3194: 3192: 3188: 3171: 3166: 3162: 3155: 3154: 3150: 3144: 3140: 3128: 3127: 3123: 3115: 3114: 3110: 3106: 3104: 3091: 3090: 3086: 3084: 3081: 3080: 3073: 3066: 3059: 3053:. In addition, 3052: 3045: 3038: 3031: 3024: 3017: 3010: 3003: 2996: 2989: 2982: 2966: 2959: 2952: 2945: 2938: 2931: 2924: 2917: 2909:hybrid-pi model 2905: 2897: 2890: 2850: 2849: 2845: 2840: 2835: 2829: 2825: 2823: 2820: 2819: 2795: 2794: 2790: 2781: 2777: 2776: 2770: 2766: 2764: 2762: 2759: 2758: 2734: 2733: 2729: 2720: 2716: 2715: 2709: 2705: 2703: 2698: 2695: 2694: 2671: 2667: 2657: 2656: 2652: 2651: 2646: 2644: 2641: 2640: 2634: 2628: 2622: 2616: 2606: 2599: 2592: 2585: 2573: 2566: 2559: 2541: 2527: 2520: 2513: 2506: 2491: 2484: 2377:Ideal feedback 2326: 2319: 2312: 2297: 2290: 2247: 2243: 2233: 2223: 2219: 2213: 2209: 2208: 2206: 2197: 2193: 2182: 2178: 2172: 2168: 2166: 2164: 2161: 2160: 2134: 2130: 2118: 2114: 2112: 2109: 2108: 2087: 2083: 2077: 2073: 2064: 2060: 2054: 2050: 2041: 2037: 2035: 2032: 2031: 2010: 2006: 2000: 1996: 1987: 1983: 1977: 1973: 1964: 1960: 1958: 1955: 1954: 1948: 1941: 1927: 1916: 1904: 1897: 1891: 1884: 1876: 1870: 1859: 1842: 1835: 1828: 1817: 1813: 1807: 1800: 1753: 1744: 1698: 1673: 1666: 1659: 1652: 1639: 1617: 1616: 1596: 1592: 1583: 1579: 1566: 1561: 1551: 1547: 1538: 1534: 1521: 1515: 1511: 1509: 1500: 1499: 1490: 1486: 1474: 1470: 1465: 1452: 1446: 1442: 1440: 1431: 1430: 1418: 1414: 1409: 1389: 1383: 1379: 1369: 1359: 1355: 1350: 1330: 1324: 1320: 1319: 1317: 1308: 1307: 1298: 1294: 1284: 1278: 1274: 1272: 1265: 1250: 1246: 1242: 1240: 1237: 1236: 1227: 1220: 1205: 1174: 1170: 1165: 1152: 1146: 1142: 1140: 1122: 1118: 1116: 1113: 1112: 1093: 1071: 1067: 1053: 1050: 1049: 1030: 1026: 1015: 1012: 1011: 987: 982: 979: 978: 960: 957: 956: 934: 930: 917: 911: 907: 905: 903: 900: 899: 880: 876: 874: 871: 870: 863: 844: 831: 809: 802: 794: 787: 780: 749: 745: 732: 726: 722: 720: 709: 705: 699: 695: 693: 684: 680: 678: 675: 674: 669: 641: 637: 628: 624: 612: 608: 587: 583: 581: 578: 577: 548: 544: 529: 525: 516: 512: 503: 499: 497: 494: 493: 488: 460: 456: 441: 437: 425: 419: 416: 415: 410: 388: 384: 376: 373: 372: 346: 333: 329: 320: 316: 314: 311: 310: 305: 282: 274:feedback factor 271: 261: 250: 242: 214: 115:MOS transistors 103: 70: 17: 12: 11: 5: 7786: 7776: 7775: 7770: 7755: 7754: 7743:. Linear Audio 7728: 7724:Wireless World 7711: 7674: 7642: 7610: 7578: 7556: 7527: 7520: 7500: 7490: 7464: 7454: 7448: 7444: 7438: 7434:, and finding 7430: 7423: 7417: 7406: 7399: 7379: 7374: 7370: 7362: 7348: 7326: 7319: 7299: 7292: 7272: 7250: 7235: 7213: 7203: 7177: 7158:(4): 455–463. 7138: 7131: 7105: 7098: 7072: 7065: 7038: 6995:(4): 298–302. 6967: 6960: 6940: 6937:on 2014-12-30. 6911: 6904: 6878: 6871: 6849: 6839: 6819: 6809: 6787: 6780: 6760: 6745: 6737:Analog Devices 6721: 6714: 6688: 6681: 6663: 6660:on 2016-06-05. 6638: 6631: 6611: 6600: 6593: 6573: 6564: 6561:on 2014-10-06. 6535: 6494: 6487: 6467: 6460: 6440: 6433: 6413: 6407:978-8120319523 6406: 6381: 6379: 6376: 6375: 6374: 6369: 6364: 6362:Pole splitting 6359: 6354: 6348: 6335: 6332:Miller theorem 6329: 6324: 6319: 6313: 6307: 6302: 6297: 6290: 6287: 6261:effect of the 6251:common emitter 6246: 6243: 6228: 6225: 6221: 6197: 6177: 6157: 6137: 6117: 6097: 6077: 6063:- resistance. 6052: 6032: 6012: 5992: 5972: 5957: 5956: 5940: 5936: 5930: 5926: 5922: 5919: 5913: 5909: 5896: 5880: 5876: 5870: 5866: 5862: 5859: 5853: 5849: 5836: 5820: 5816: 5810: 5806: 5802: 5799: 5793: 5789: 5783: 5776: 5772: 5766: 5762: 5756: 5751: 5748: 5744: 5733: 5730: 5727: 5719: 5718: 5707: 5702: 5698: 5692: 5688: 5684: 5681: 5678: 5673: 5669: 5658: 5647: 5642: 5638: 5632: 5628: 5624: 5621: 5618: 5613: 5609: 5598: 5582: 5578: 5572: 5568: 5564: 5561: 5555: 5551: 5545: 5538: 5534: 5528: 5524: 5518: 5513: 5510: 5506: 5495: 5492: 5489: 5484:Series-Series( 5481: 5480: 5469: 5464: 5460: 5454: 5450: 5446: 5443: 5440: 5435: 5431: 5420: 5404: 5400: 5394: 5390: 5386: 5383: 5377: 5373: 5360: 5344: 5340: 5334: 5330: 5326: 5323: 5317: 5313: 5307: 5300: 5296: 5290: 5286: 5280: 5275: 5272: 5268: 5257: 5254: 5251: 5247: 5246: 5230: 5226: 5220: 5216: 5212: 5209: 5203: 5199: 5186: 5175: 5170: 5166: 5160: 5156: 5152: 5149: 5146: 5141: 5137: 5126: 5110: 5106: 5100: 5096: 5092: 5089: 5083: 5079: 5073: 5066: 5062: 5056: 5052: 5046: 5041: 5038: 5034: 5023: 5020: 5017: 5013: 5012: 5009: 5006: 5003: 5002:Output Signal 5000: 4999:Source Signal 4997: 4985: 4982: 4980:simulations). 4950: 4946: 4926: 4919: 4912: 4905: 4898: 4891: 4884: 4877: 4870: 4855: 4848: 4822: 4819: 4818: 4817: 4816: 4815: 4804: 4792: 4787: 4783: 4777: 4774: 4769: 4761: 4758: 4753: 4744: 4741: 4736: 4732: 4724: 4719: 4712: 4707: 4683: 4677: 4676: 4675: 4674: 4663: 4657: 4651: 4646: 4642: 4636: 4633: 4628: 4624: 4618: 4615: 4610: 4606: 4598: 4593: 4586: 4581: 4561: 4554: 4547: 4540: 4533: 4526: 4519: 4512: 4501: 4493: 4490: 4485: 4481: 4470: 4463: 4444: 4430: 4429: 4428: 4427: 4416: 4404: 4401: 4396: 4389: 4386: 4380: 4375: 4372: 4366: 4362: 4356: 4350: 4347: 4342: 4324: 4317: 4310: 4303: 4296: 4286: 4282: 4274: 4271: 4244: 4235: 4227: 4226: 4225: 4224: 4213: 4204: 4198: 4194: 4190: 4187: 4184: 4180: 4173: 4170: 4165: 4159: 4152: 4148: 4142: 4138: 4132: 4129: 4126: 4123: 4120: 4114: 4111: 4106: 4088: 4081: 4075: 4068: 4062: 4055: 4049: 4048: 4047: 4046: 4035: 4026: 4023: 4020: 4015: 4011: 4008: 4000: 3997: 3992: 3985: 3982: 3977: 3971: 3966: 3962: 3940: 3933: 3925: 3919: 3909: 3900: 3892: 3891: 3890: 3889: 3878: 3869: 3866: 3861: 3856: 3850: 3846: 3842: 3839: 3836: 3832: 3828: 3821: 3817: 3811: 3807: 3801: 3798: 3795: 3792: 3789: 3783: 3780: 3775: 3757: 3751: 3745: 3738: 3732: 3725: 3719: 3718: 3717: 3716: 3705: 3696: 3693: 3690: 3685: 3681: 3678: 3672: 3669: 3664: 3658: 3654: 3650: 3645: 3641: 3620:Miller theorem 3615: 3608: 3600: 3594: 3580: 3577: 3557: 3554: 3549: 3545: 3541: 3538: 3537: 3536: 3535: 3534: 3533: 3522: 3510: 3507: 3502: 3492: 3487: 3483: 3478: 3474: 3467: 3463: 3457: 3454: 3447: 3444: 3439: 3433: 3427: 3424: 3419: 3391: 3388: 3383: 3376: 3373: 3367: 3362: 3359: 3352: 3349: 3344: 3338: 3332: 3329: 3324: 3306: 3300: 3293: 3290: 3289: 3288: 3287: 3286: 3275: 3268: 3259: 3256: 3253: 3245: 3240: 3236: 3231: 3228: 3224: 3217: 3212: 3208: 3201: 3197: 3191: 3186: 3180: 3177: 3174: 3170: 3165: 3158: 3153: 3147: 3143: 3139: 3131: 3126: 3118: 3113: 3109: 3103: 3097: 3094: 3089: 3071: 3064: 3057: 3050: 3043: 3036: 3029: 3022: 3015: 3008: 3001: 2994: 2987: 2980: 2974:open-loop gain 2965: 2962: 2957: 2950: 2943: 2936: 2929: 2922: 2915: 2904: 2901: 2895: 2888: 2872: 2871: 2853: 2848: 2843: 2838: 2832: 2828: 2816: 2798: 2793: 2789: 2784: 2780: 2773: 2769: 2755: 2737: 2732: 2728: 2723: 2719: 2712: 2708: 2702: 2691: 2674: 2670: 2666: 2660: 2655: 2650: 2636: 2635: 2632: 2629: 2626: 2623: 2620: 2617: 2614: 2604: 2597: 2590: 2583: 2571: 2564: 2557: 2539: 2525: 2518: 2511: 2504: 2490: 2487: 2482: 2450: 2449: 2446: 2443: 2440: 2437: 2433: 2432: 2429: 2426: 2423: 2420: 2416: 2415: 2412: 2409: 2406: 2403: 2399: 2398: 2395: 2392: 2389: 2386: 2382: 2381: 2378: 2375: 2372: 2369: 2325: 2322: 2317: 2310: 2295: 2288: 2270: 2269: 2258: 2250: 2246: 2242: 2239: 2236: 2231: 2226: 2222: 2216: 2212: 2205: 2200: 2196: 2192: 2181: 2171: 2154: 2153: 2142: 2137: 2133: 2129: 2126: 2121: 2117: 2106: 2095: 2090: 2086: 2080: 2076: 2072: 2063: 2057: 2053: 2049: 2044: 2040: 2029: 2018: 2013: 2009: 2003: 1999: 1995: 1986: 1980: 1976: 1972: 1963: 1946: 1939: 1930: 1929: 1925: 1914: 1902: 1895: 1889: 1882: 1874: 1868: 1857: 1850: 1849: 1840: 1833: 1826: 1815: 1811: 1805: 1798: 1784: 1783: 1765:, such as the 1749: 1740: 1697: 1694: 1672: 1671:Multiple poles 1669: 1664: 1657: 1650: 1637: 1631: 1630: 1615: 1608: 1595: 1591: 1586: 1582: 1578: 1575: 1572: 1569: 1565: 1560: 1557: 1554: 1550: 1546: 1541: 1537: 1533: 1530: 1527: 1524: 1518: 1514: 1508: 1505: 1503: 1501: 1493: 1489: 1485: 1482: 1473: 1468: 1464: 1461: 1458: 1455: 1449: 1445: 1439: 1436: 1434: 1432: 1426: 1417: 1412: 1408: 1405: 1402: 1399: 1396: 1392: 1386: 1382: 1378: 1375: 1372: 1367: 1358: 1353: 1349: 1346: 1343: 1340: 1337: 1333: 1327: 1323: 1316: 1313: 1311: 1309: 1297: 1293: 1290: 1287: 1277: 1271: 1268: 1266: 1264: 1261: 1258: 1249: 1245: 1244: 1225: 1218: 1203: 1197: 1196: 1185: 1173: 1168: 1164: 1161: 1158: 1155: 1149: 1145: 1139: 1136: 1133: 1130: 1121: 1092: 1089: 1088: 1087: 1070: 1066: 1063: 1060: 1057: 1046: 1029: 1025: 1022: 1019: 1005: 994: 990: 986: 975: 964: 953: 933: 929: 926: 923: 920: 910: 896: 879: 867:Open-loop gain 862: 859: 842: 829: 807: 800: 792: 785: 778: 772: 771: 760: 748: 744: 741: 738: 735: 725: 719: 708: 698: 692: 683: 667: 661: 660: 649: 640: 636: 627: 623: 620: 611: 607: 604: 601: 598: 595: 586: 571: 570: 559: 556: 547: 543: 540: 537: 528: 524: 515: 511: 502: 486: 480: 479: 468: 459: 455: 452: 449: 440: 436: 432: 424: 408: 387: 383: 380: 369: 368: 357: 353: 345: 341: 332: 328: 319: 303: 280: 269: 264:open-loop gain 259: 249: 248:Gain reduction 246: 241: 238: 213: 210: 209: 208: 205: 194: 191: 184: 183: 176: 173: 170: 167: 164: 102: 99: 98: 97: 90: 72: 68: 15: 9: 6: 4: 3: 2: 7785: 7774: 7771: 7769: 7766: 7765: 7763: 7739: 7732: 7725: 7721: 7715: 7700:on 2013-06-19 7696: 7692: 7685: 7678: 7671: 7661:on 2015-11-21 7660: 7656: 7652: 7646: 7639: 7628: 7624: 7617: 7615: 7607: 7596: 7592: 7585: 7583: 7575: 7567: 7560: 7553: 7541: 7537: 7531: 7523: 7521:9780792376439 7517: 7513: 7512: 7504: 7497: 7493: 7487: 7483: 7479: 7475: 7468: 7458: 7451: 7437: 7433: 7426: 7416: 7410: 7402: 7396: 7392: 7391: 7383: 7366: 7359: 7352: 7344: 7343: 7335: 7333: 7331: 7322: 7320:0-19-514251-9 7316: 7312: 7311: 7303: 7295: 7293:0-471-32168-0 7289: 7285: 7284: 7276: 7269: 7265: 7262: 7261: 7254: 7247: 7246: 7239: 7232: 7228: 7225: 7224: 7217: 7210: 7206: 7204:9780070329225 7200: 7196: 7191: 7190: 7181: 7173: 7169: 7165: 7161: 7157: 7153: 7149: 7142: 7134: 7132:9780792376439 7128: 7124: 7120: 7116: 7109: 7101: 7099:9781420037272 7095: 7091: 7087: 7083: 7076: 7068: 7066:9781139485234 7062: 7058: 7054: 7050: 7042: 7034: 7028: 7020: 7016: 7012: 7008: 7003: 6998: 6994: 6990: 6983: 6976: 6974: 6972: 6963: 6961:9780792376439 6957: 6953: 6952: 6944: 6933: 6929: 6922: 6915: 6907: 6905:9780387680309 6901: 6897: 6893: 6889: 6882: 6874: 6872:9781420058826 6868: 6864: 6860: 6853: 6846: 6842: 6840:9780792376439 6836: 6832: 6831: 6823: 6816: 6812: 6810:9781259029844 6806: 6802: 6798: 6791: 6783: 6781:0-387-25746-2 6777: 6773: 6772: 6764: 6757: 6756: 6749: 6742: 6738: 6731: 6725: 6717: 6715:9780521370950 6711: 6707: 6702: 6701: 6692: 6684: 6682:9780240526133 6678: 6674: 6667: 6656: 6649: 6642: 6634: 6632:9780023749100 6628: 6624: 6623: 6615: 6604: 6596: 6594:0-471-05319-8 6590: 6586: 6585: 6577: 6568: 6557: 6553: 6546: 6539: 6524: 6520: 6516: 6512: 6505: 6498: 6490: 6488:9780750678445 6484: 6480: 6479: 6471: 6463: 6461:0-7923-7643-9 6457: 6453: 6452: 6444: 6436: 6434:0-471-13476-7 6430: 6426: 6425: 6417: 6409: 6403: 6399: 6395: 6394: 6386: 6382: 6373: 6372:Step response 6370: 6368: 6365: 6363: 6360: 6358: 6355: 6352: 6349: 6347: 6343: 6339: 6336: 6333: 6330: 6328: 6325: 6323: 6320: 6317: 6314: 6311: 6308: 6306: 6303: 6301: 6298: 6296: 6293: 6292: 6286: 6283: 6278: 6276: 6272: 6266: 6264: 6260: 6256: 6252: 6242: 6226: 6223: 6219: 6209: 6195: 6175: 6168:- output and 6155: 6135: 6115: 6095: 6075: 6067: 6064: 6050: 6030: 6010: 5990: 5970: 5962: 5938: 5934: 5928: 5924: 5920: 5917: 5911: 5907: 5897: 5878: 5874: 5868: 5864: 5860: 5857: 5851: 5847: 5837: 5818: 5814: 5808: 5804: 5800: 5797: 5791: 5787: 5781: 5774: 5770: 5764: 5760: 5754: 5749: 5746: 5742: 5734: 5731: 5728: 5725: 5722:Shunt-Shunt ( 5721: 5720: 5700: 5696: 5690: 5686: 5682: 5679: 5671: 5667: 5659: 5640: 5636: 5630: 5626: 5622: 5619: 5611: 5607: 5599: 5580: 5576: 5570: 5566: 5562: 5559: 5553: 5549: 5543: 5536: 5532: 5526: 5522: 5516: 5511: 5508: 5504: 5496: 5493: 5490: 5487: 5483: 5482: 5462: 5458: 5452: 5448: 5444: 5441: 5433: 5429: 5421: 5402: 5398: 5392: 5388: 5384: 5381: 5375: 5371: 5361: 5342: 5338: 5332: 5328: 5324: 5321: 5315: 5311: 5305: 5298: 5294: 5288: 5284: 5278: 5273: 5270: 5266: 5258: 5255: 5252: 5249: 5248: 5228: 5224: 5218: 5214: 5210: 5207: 5201: 5197: 5187: 5168: 5164: 5158: 5154: 5150: 5147: 5139: 5135: 5127: 5108: 5104: 5098: 5094: 5090: 5087: 5081: 5077: 5071: 5064: 5060: 5054: 5050: 5044: 5039: 5036: 5032: 5024: 5021: 5018: 5015: 5014: 5010: 5007: 5004: 5001: 4998: 4995: 4994: 4989: 4981: 4979: 4975: 4972:, and use of 4971: 4967: 4963: 4958: 4956: 4944: 4939: 4935: 4932: 4925: 4918: 4911: 4904: 4897: 4890: 4883: 4876: 4869: 4865: 4859: 4854: 4847: 4843: 4838: 4832: 4827: 4802: 4785: 4781: 4775: 4767: 4759: 4751: 4734: 4730: 4717: 4705: 4695: 4694: 4693: 4692: 4691: 4689: 4682: 4661: 4644: 4640: 4634: 4626: 4608: 4604: 4591: 4579: 4569: 4568: 4567: 4566: 4565: 4560: 4553: 4546: 4539: 4532: 4525: 4518: 4511: 4507: 4500: 4489: 4479: 4474: 4473:in Figure 3. 4469: 4462: 4456: 4454: 4450: 4443: 4439: 4435: 4414: 4394: 4378: 4373: 4370: 4364: 4360: 4354: 4340: 4332: 4331: 4330: 4329: 4328: 4323: 4316: 4309: 4302: 4295: 4290: 4280: 4270: 4267: 4265: 4261: 4257: 4253: 4248: 4243: 4239: 4232: 4211: 4202: 4196: 4192: 4188: 4185: 4182: 4178: 4163: 4157: 4150: 4146: 4140: 4136: 4130: 4124: 4121: 4104: 4096: 4095: 4094: 4093: 4092: 4087: 4080: 4074: 4067: 4061: 4054: 4033: 4013: 4009: 4006: 3990: 3975: 3969: 3964: 3960: 3952: 3951: 3950: 3949: 3948: 3946: 3939: 3932: 3928: 3918: 3913: 3908: 3904: 3897: 3876: 3859: 3854: 3848: 3844: 3840: 3837: 3834: 3830: 3826: 3819: 3815: 3809: 3805: 3799: 3793: 3790: 3773: 3765: 3764: 3763: 3762: 3761: 3756: 3750: 3744: 3737: 3731: 3724: 3703: 3683: 3679: 3676: 3662: 3656: 3652: 3648: 3643: 3639: 3631: 3630: 3629: 3628: 3627: 3625: 3621: 3614: 3607: 3603: 3593: 3588: 3586: 3576: 3573: 3571: 3562: 3553: 3520: 3500: 3485: 3481: 3476: 3472: 3465: 3461: 3455: 3452: 3437: 3431: 3417: 3409: 3408: 3381: 3365: 3360: 3357: 3342: 3336: 3322: 3314: 3313: 3312: 3311: 3310: 3305: 3299: 3273: 3266: 3257: 3254: 3251: 3238: 3234: 3229: 3226: 3222: 3215: 3210: 3206: 3199: 3195: 3189: 3184: 3178: 3175: 3172: 3168: 3163: 3151: 3145: 3141: 3137: 3124: 3111: 3107: 3101: 3087: 3079: 3078: 3077: 3076: 3075: 3070: 3063: 3056: 3049: 3042: 3035: 3028: 3021: 3014: 3007: 3000: 2993: 2986: 2979: 2975: 2970: 2961: 2956: 2949: 2942: 2935: 2928: 2921: 2914: 2910: 2894: 2887: 2883: 2878: 2870: 2846: 2830: 2826: 2817: 2815: 2791: 2787: 2782: 2778: 2771: 2767: 2756: 2754: 2730: 2726: 2721: 2717: 2710: 2706: 2700: 2692: 2690: 2672: 2668: 2664: 2653: 2648: 2638: 2630: 2624: 2618: 2612: 2611: 2608: 2603: 2596: 2589: 2582: 2577: 2570: 2563: 2556: 2547: 2543: 2538: 2534: 2529: 2524: 2517: 2510: 2503: 2498: 2496: 2486: 2481: 2473: 2468: 2464: 2462: 2458: 2447: 2444: 2441: 2438: 2435: 2434: 2430: 2427: 2424: 2421: 2418: 2417: 2413: 2410: 2407: 2404: 2401: 2400: 2396: 2393: 2390: 2387: 2384: 2383: 2379: 2376: 2373: 2370: 2367: 2366: 2363: 2359: 2357: 2352: 2350: 2345: 2341: 2340: 2330: 2321: 2316: 2309: 2305: 2301: 2294: 2287: 2283: 2279: 2275: 2256: 2248: 2244: 2240: 2237: 2234: 2229: 2224: 2220: 2214: 2210: 2203: 2198: 2194: 2190: 2179: 2169: 2159: 2158: 2157: 2140: 2135: 2131: 2127: 2124: 2119: 2115: 2107: 2093: 2088: 2084: 2078: 2074: 2070: 2061: 2055: 2051: 2047: 2042: 2038: 2030: 2016: 2011: 2007: 2001: 1997: 1993: 1984: 1978: 1974: 1970: 1961: 1953: 1952: 1951: 1949: 1942: 1935: 1924: 1920: 1913: 1909: 1905: 1898: 1888: 1881: 1877: 1867: 1863: 1856: 1852: 1851: 1847: 1843: 1836: 1829: 1822: 1818: 1804: 1797: 1793: 1792: 1791: 1789: 1780: 1776: 1775: 1774: 1772: 1768: 1764: 1757: 1752: 1748: 1743: 1739: 1735: 1731: 1726: 1722: 1720: 1716: 1712: 1707: 1703: 1693: 1691: 1687: 1686:step response 1683: 1679: 1668: 1663: 1656: 1649: 1645: 1644: 1636: 1613: 1606: 1593: 1584: 1580: 1576: 1573: 1570: 1563: 1558: 1555: 1552: 1548: 1539: 1535: 1531: 1528: 1525: 1516: 1512: 1506: 1504: 1491: 1487: 1483: 1480: 1471: 1466: 1462: 1459: 1456: 1453: 1447: 1443: 1437: 1435: 1415: 1410: 1406: 1403: 1400: 1397: 1390: 1384: 1380: 1376: 1373: 1370: 1356: 1351: 1347: 1344: 1341: 1338: 1331: 1325: 1321: 1314: 1312: 1295: 1291: 1288: 1285: 1275: 1269: 1267: 1259: 1247: 1235: 1234: 1233: 1231: 1224: 1217: 1213: 1209: 1202: 1183: 1171: 1166: 1162: 1159: 1156: 1153: 1147: 1143: 1137: 1131: 1119: 1111: 1110: 1109: 1107: 1097: 1068: 1064: 1061: 1058: 1055: 1047: 1027: 1023: 1020: 1017: 1009: 1006: 992: 988: 984: 977:Noise gain = 976: 962: 954: 931: 927: 924: 921: 918: 908: 897: 877: 868: 865: 864: 858: 856: 852: 848: 841: 837: 836: 828: 824: 819: 817: 813: 806: 799: 791: 784: 777: 758: 746: 742: 739: 736: 733: 723: 717: 706: 696: 690: 681: 673: 672: 671: 666: 647: 638: 634: 625: 621: 609: 605: 602: 599: 596: 584: 576: 575: 574: 573:Rearranging: 557: 545: 541: 538: 535: 526: 513: 509: 500: 492: 491: 490: 485: 466: 457: 453: 450: 447: 438: 434: 430: 422: 414: 413: 412: 407: 385: 381: 378: 355: 351: 343: 339: 330: 326: 317: 309: 308: 307: 302: 297: 294: 290: 286: 279: 275: 268: 265: 258: 255: 245: 237: 235: 231: 227: 223: 219: 206: 203: 199: 195: 192: 189: 188: 187: 182:of amplifier. 181: 180:step response 177: 174: 171: 168: 165: 162: 158: 157: 156: 153: 150: 148: 144: 143:Harry Nyquist 141:developed by 140: 136: 132: 128: 124: 120: 116: 112: 108: 95: 91: 88: 84: 80: 77: 73: 67: 64: 60: 56: 55: 54: 51: 49: 48:step response 45: 41: 38: 34: 30: 21: 7745:. Retrieved 7731: 7723: 7719: 7714: 7702:. Retrieved 7695:the original 7690: 7677: 7669: 7663:. Retrieved 7659:the original 7654: 7645: 7636: 7630:. Retrieved 7626: 7604: 7598:. Retrieved 7595:passlabs.com 7594: 7572: 7559: 7550: 7544:. Retrieved 7539: 7530: 7510: 7503: 7495: 7481: 7477: 7467: 7457: 7442: 7435: 7428: 7421: 7414: 7409: 7389: 7382: 7365: 7351: 7341: 7309: 7302: 7282: 7275: 7259: 7253: 7244: 7238: 7222: 7216: 7208: 7188: 7180: 7155: 7151: 7141: 7122: 7118: 7108: 7089: 7085: 7075: 7056: 7052: 7041: 7027:cite journal 6992: 6988: 6950: 6943: 6932:the original 6927: 6914: 6895: 6891: 6881: 6862: 6852: 6844: 6829: 6822: 6814: 6800: 6790: 6770: 6763: 6754: 6748: 6740: 6724: 6699: 6691: 6672: 6666: 6655:the original 6641: 6621: 6614: 6603: 6583: 6576: 6567: 6556:the original 6551: 6538: 6526:. Retrieved 6514: 6510: 6497: 6477: 6470: 6450: 6443: 6423: 6416: 6397: 6392: 6385: 6367:Return ratio 6357:Phase margin 6281: 6279: 6267: 6248: 6211:For example 6210: 6068: 6065: 5963: 5960: 4987: 4970:Choma method 4959: 4942: 4941:However, if 4940: 4936: 4930: 4923: 4916: 4909: 4902: 4895: 4888: 4881: 4874: 4867: 4863: 4860: 4852: 4845: 4839: 4836: 4830: 4680: 4678: 4558: 4551: 4544: 4537: 4530: 4523: 4516: 4509: 4498: 4495: 4477: 4475: 4467: 4460: 4457: 4448: 4441: 4437: 4433: 4431: 4321: 4314: 4307: 4300: 4293: 4291: 4278: 4276: 4268: 4263: 4249: 4241: 4234: 4230: 4228: 4085: 4078: 4072: 4065: 4059: 4052: 4050: 3937: 3930: 3923: 3916: 3914: 3906: 3899: 3895: 3893: 3754: 3748: 3742: 3735: 3729: 3722: 3720: 3612: 3605: 3598: 3591: 3589: 3582: 3574: 3567: 3548:. Notation β 3539: 3303: 3297: 3295: 3068: 3061: 3054: 3047: 3040: 3033: 3026: 3019: 3012: 3005: 2998: 2991: 2984: 2977: 2973: 2971: 2967: 2954: 2947: 2940: 2933: 2926: 2919: 2912: 2906: 2892: 2885: 2881: 2818: 2757: 2693: 2639: 2601: 2594: 2587: 2580: 2568: 2561: 2554: 2552: 2536: 2530: 2522: 2515: 2508: 2501: 2499: 2492: 2479: 2477: 2472:shunt-series 2471: 2470:Figure 3: A 2453: 2448:h-parameter 2431:z-parameter 2414:y-parameter 2397:g-parameter 2360: 2353: 2338: 2335: 2314: 2307: 2303: 2299: 2292: 2285: 2281: 2273: 2271: 2155: 1944: 1937: 1933: 1931: 1922: 1918: 1911: 1907: 1900: 1893: 1886: 1879: 1872: 1865: 1861: 1854: 1845: 1838: 1831: 1824: 1820: 1809: 1802: 1795: 1787: 1785: 1778: 1760: 1755: 1750: 1746: 1741: 1737: 1733: 1718: 1714: 1705: 1702:Introduction 1701: 1699: 1674: 1661: 1654: 1647: 1641: 1634: 1632: 1229: 1222: 1215: 1200: 1198: 1105: 1102: 854: 850: 846: 839: 833: 826: 822: 820: 812:Nyquist plot 804: 797: 789: 782: 775: 773: 670:is given by 664: 662: 572: 483: 481: 405: 370: 300: 298: 277: 273: 266: 263: 256: 253: 251: 243: 233: 215: 201: 197: 185: 178:Can control 154: 151: 107:vacuum tubes 104: 93: 78: 75: 65: 58: 52: 32: 28: 26: 7691:Stereophile 6801:VLSI Design 6003:- current, 5726:amplifier) 5488:amplifier) 4453:found above 1928:, to zero." 1794:"Variables 1728:A possible 1653:) = 10, so 1230:closed-loop 135:oscillation 83:attenuating 7762:Categories 7665:2016-04-18 7632:2016-04-18 7600:2016-04-18 7546:2016-04-18 7491:0072320990 7358:unilateral 6646:Lu, L. H. 6528:January 2, 6481:. Newnes. 6275:audiophile 6245:Distortion 6108:- voltage, 6023:- voltage, 3626:provides: 1706:autonomous 816:Bode plots 781:≫ 1, then 289:capacitors 226:distortion 131:distortion 94:subtractor 37:electronic 7606:feedback. 7574:products. 6997:CiteSeerX 6305:Bode plot 6031:β 5925:β 5865:β 5805:β 5687:β 5627:β 5567:β 5449:β 5389:β 5329:β 5215:β 5155:β 5095:β 4641:∥ 4506:Ohm's law 4379:β 4189:β 4010:β 3841:β 3680:β 3366:β 3252:β 3227:π 3173:β 3169:β 3108:β 3060:= −(β+1) 2701:− 2344:two-ports 2238:− 1853:The term 1682:overshoot 1577:β 1532:β 1484:β 1377:β 1292:β 1106:open-loop 1065:⋅ 1062:β 1024:⋅ 1021:β 1018:− 1008:Loop gain 993:β 963:β 928:⋅ 925:β 835:loop gain 743:⋅ 740:β 635:⋅ 606:⋅ 603:β 542:⋅ 539:β 536:− 454:⋅ 451:β 448:− 382:⋅ 379:β 340:⋅ 293:inductors 161:impedance 119:nonlinear 87:filtering 59:amplifier 40:amplifier 7747:19 March 7264:Archived 7227:Archived 7019:10154732 6584:Feedback 6289:See also 5983:- gain, 5732:Voltage 5729:Current 5494:Current 5491:Voltage 5256:Current 5253:Current 5022:Voltage 5019:Voltage 4447:is the 4434:division 4256:Thévenin 4240:, where 3905:, where 2495:two-port 2436:Voltage 2385:Current 1779:a priori 431:′ 352:′ 272:and the 230:repeater 101:Overview 35:) is an 7726:, 1978. 7160:Bibcode 6259:masking 4478:emitter 2439:Series 2425:Series 2422:Series 2391:Series 1769:or the 1684:in its 1678:ringing 1206:is the 212:History 125:trades 7518: 7488: 7397: 7317: 7290: 7201: 7129: 7096: 7063: 7017: 6999: 6958: 6902: 6869: 6837: 6807: 6778: 6712: 6679: 6629: 6591: 6485: 6458: 6431: 6404: 4968:, the 4864:unless 4800: 4659: 4449:loaded 4432:where 4412: 4252:Norton 4209: 4051:where 4031: 3874: 3721:where 3701: 3518: 3271: 3025:. Let 3004:, and 2939:= 1 / 2858: 2442:Shunt 2408:Shunt 2405:Shunt 2388:Shunt 2282:et al. 1788:et al. 1756:et al. 1715:global 1208:cutoff 1199:where 186:Cons: 155:Pros: 137:. The 117:) are 7741:(PDF) 7704:9 May 7698:(PDF) 7687:(PDF) 7569:(PDF) 7015:S2CID 6985:(PDF) 6935:(PDF) 6924:(PDF) 6733:(PDF) 6658:(PDF) 6651:(PDF) 6559:(PDF) 6548:(PDF) 6507:(PDF) 4978:SPICE 4955:Spice 4438:shunt 2445:VCVS 2428:VCCS 2411:CCVS 2394:CCCS 2298:= 1, 1719:local 853:, or 825:= −β 61:with 7749:2013 7706:2007 7516:ISBN 7486:ISBN 7395:ISBN 7315:ISBN 7288:ISBN 7199:ISBN 7127:ISBN 7094:ISBN 7061:ISBN 7033:link 6956:ISBN 6900:ISBN 6867:ISBN 6835:ISBN 6805:ISBN 6776:ISBN 6710:ISBN 6677:ISBN 6627:ISBN 6589:ISBN 6530:2013 6483:ISBN 6456:ISBN 6429:ISBN 6402:ISBN 6344:and 4264:same 3544:= −g 3074:is: 2932:and 2891:and 2586:and 2567:and 1680:and 127:gain 89:it), 63:gain 31:(or 7722:”, 7627:EDN 7447:/ I 7439:out 7195:986 7168:doi 7007:doi 6519:doi 6282:all 6271:THD 4856:out 4557:|| 4529:|| 4508:as 4488:). 4320:|| 4313:|| 4254:or 4056:out 3920:out 3726:out 3595:out 3046:|| 3039:|| 2925:|| 1814:, x 1210:or 774:If 701:out 589:out 550:out 505:out 462:out 390:out 322:out 291:or 228:in 145:of 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3868:n 3865:i 3860:R 3855:) 3849:v 3845:A 3838:+ 3835:1 3831:( 3827:= 3820:x 3816:I 3810:x 3806:V 3800:= 3797:) 3794:b 3791:f 3788:( 3782:n 3779:i 3774:R 3755:R 3752:x 3749:I 3746:v 3743:A 3736:v 3733:v 3730:A 3723:v 3704:, 3695:t 3692:u 3689:o 3684:v 3677:+ 3671:n 3668:i 3663:R 3657:x 3653:I 3649:= 3644:x 3640:V 3613:R 3606:R 3601:x 3599:V 3592:V 3521:, 3509:L 3506:O 3501:A 3491:f 3486:R 3482:+ 3477:2 3473:R 3466:2 3462:R 3456:+ 3453:1 3446:L 3443:O 3438:A 3432:= 3426:B 3423:F 3418:A 3390:L 3387:O 3382:A 3375:B 3372:F 3361:+ 3358:1 3351:L 3348:O 3343:A 3337:= 3331:B 3328:F 3323:A 3307:1 3304:v 3298:g 3274:. 3267:) 3258:1 3255:+ 3244:C 3239:R 3235:+ 3230:2 3223:r 3216:+ 3207:R 3200:1 3196:R 3190:( 3185:) 3179:1 3176:+ 3164:( 3157:C 3152:R 3146:m 3142:g 3138:= 3130:S 3125:i 3117:B 3112:i 3102:= 3096:L 3093:O 3088:A 3069:A 3065:B 3062:i 3058:2 3055:i 3048:r 3044:B 3041:R 3034:R 3030:1 3027:R 3023:π 3020:v 3016:1 3013:v 3006:r 3002:B 2999:R 2992:R 2985:g 2978:g 2955:g 2948:R 2941:g 2934:R 2930:L 2927:R 2920:R 2916:3 2913:R 2898:. 2896:2 2893:R 2889:f 2886:R 2882:L 2852:f 2847:R 2842:| 2837:| 2831:2 2827:R 2797:f 2792:R 2788:+ 2783:2 2779:R 2772:2 2768:R 2736:f 2731:R 2727:+ 2722:2 2718:R 2711:2 2707:R 2673:2 2669:R 2665:+ 2659:f 2654:R 2649:1 2631:g 2625:g 2619:g 2613:g 2605:2 2602:I 2598:1 2595:V 2591:f 2588:R 2584:2 2581:R 2572:f 2569:R 2565:2 2562:R 2558:2 2555:R 2540:2 2537:R 2526:2 2523:R 2519:f 2516:R 2512:f 2509:R 2505:f 2502:R 2483:f 2480:R 2315:a 2308:a 2304:A 2300:P 2293:a 2286:a 2274:P 2257:. 2245:a 2241:P 2235:1 2230:P 2221:a 2211:a 2204:+ 2195:a 2191:= 2184:S 2180:x 2174:O 2170:x 2141:. 2136:i 2132:x 2128:P 2125:= 2120:j 2116:x 2094:, 2089:j 2085:x 2075:a 2071:+ 2066:S 2062:x 2052:a 2048:= 2043:i 2039:x 2017:, 2012:j 2008:x 1998:a 1994:+ 1989:S 1985:x 1975:a 1971:= 1966:O 1962:x 1947:i 1940:j 1938:x 1934:P 1926:S 1923:x 1919:P 1912:a 1908:P 1903:j 1901:x 1896:i 1894:x 1887:a 1883:S 1880:x 1875:j 1873:x 1866:a 1862:P 1855:a 1846:P 1841:j 1839:x 1834:i 1832:x 1825:a 1821:P 1816:j 1812:i 1810:x 1806:O 1803:x 1799:S 1796:x 1751:i 1742:j 1738:x 1734:P 1665:C 1662:f 1655:A 1651:0 1648:A 1638:0 1635:A 1614:. 1607:) 1598:C 1594:f 1590:) 1585:0 1581:A 1574:+ 1571:1 1568:( 1564:f 1559:j 1556:+ 1553:1 1549:( 1545:) 1540:0 1536:A 1529:+ 1526:1 1523:( 1517:0 1513:A 1507:= 1492:0 1488:A 1481:+ 1476:C 1472:f 1467:/ 1463:f 1460:j 1457:+ 1454:1 1448:0 1444:A 1438:= 1425:) 1420:C 1416:f 1411:/ 1407:f 1404:j 1401:+ 1398:1 1395:( 1391:/ 1385:0 1381:A 1374:+ 1371:1 1366:) 1361:C 1357:f 1352:/ 1348:f 1345:j 1342:+ 1339:1 1336:( 1332:/ 1326:0 1322:A 1315:= 1296:A 1289:+ 1286:1 1276:A 1270:= 1263:) 1260:f 1257:( 1248:A 1226:0 1223:A 1219:C 1216:f 1204:C 1201:f 1184:, 1176:C 1172:f 1167:/ 1163:f 1160:j 1157:+ 1154:1 1148:0 1144:A 1138:= 1135:) 1132:f 1129:( 1120:A 1069:A 1059:+ 1056:1 1028:A 989:/ 985:1 932:A 922:+ 919:1 909:A 878:A 840:A 827:A 823:L 805:A 798:A 790:A 783:A 776:A 759:. 747:A 737:+ 734:1 724:A 718:= 707:V 697:V 691:= 682:A 665:A 648:. 639:A 626:V 622:= 619:) 610:A 600:+ 597:1 594:( 585:V 558:. 555:) 546:V 527:V 523:( 514:A 510:= 501:V 467:. 458:V 439:V 435:= 423:V 406:V 386:V 356:. 344:V 331:A 327:= 318:V 278:A 267:A 257:A 79:β 71:, 66:A

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