1933:
689:
1928:{\displaystyle {\begin{aligned}V_{\mathrm {L} }={}&V_{\mathrm {AC} }={\frac {V_{\mathrm {AC_{p}} }}{\sqrt {2}}}\quad {\text{(ignoring diode drop and losses)}}\\V_{\mathrm {DC} }={}&{\frac {1}{T}}\int _{0}^{T}\!V_{\mathrm {L} }(t)\,dt={\frac {V_{\mathrm {AC_{p}} }}{\pi }}{\Big }_{0}^{\pi }={\frac {V_{\mathrm {AC_{p}} }}{\pi }}\left(-\cos(\pi )--\cos(0)\right)\,={\frac {2V_{\mathrm {AC_{p}} }}{\pi }}\\V_{\mathrm {ripple-rms} }={}&{\sqrt {{\frac {1}{T}}\int _{0}^{T}\!(V_{\mathrm {L} }(t)\,-K)^{2}dt}}={\sqrt {{\frac {1}{T}}\int _{0}^{T}\!(V_{\mathrm {L} }(t)^{2}\,-2KV_{\mathrm {L} }(t)+K^{2})dt}}\\={}&{\sqrt {{\frac {1}{\pi }}\left_{0}^{\pi }}}={\sqrt {{\frac {1}{\pi }}\left({\frac {V_{\mathrm {AC_{p}} }^{2}\pi }{2}}-4KV_{\mathrm {AC_{p}} }+K^{2}\pi \right)}}\\&{\text{let }}K=V_{\mathrm {DC} },{\text{ and substitute in terms of }}V_{\mathrm {AC_{p}} },{\text{ so}}\\={}&{\sqrt {{\frac {V_{\mathrm {AC_{p}} }^{2}}{2}}-{\frac {8}{\pi ^{2}}}V_{\mathrm {AC_{p}} }^{2}+{\frac {4}{\pi ^{2}}}V_{\mathrm {AC_{p}} }^{2}}}={\sqrt {\left({\frac {V_{\mathrm {AC_{p}} }}{\sqrt {2}}}\right)^{2}-\left({\frac {2V_{\mathrm {AC_{p}} }}{\pi }}\right)^{2}}}\end{aligned}}}
5329:
4768:
4724:
5324:{\displaystyle {\begin{aligned}V_{\mathrm {DC} }={}&{\sqrt {\left({\frac {2V_{\mathrm {AC_{p}} }}{\pi }}\right)^{2}-V_{\mathrm {rms} }^{2}}}={\frac {2V_{\mathrm {AC_{p}} }}{\pi }}\quad {\text{because }}V_{\mathrm {rms} }^{2}=K{\frac {R^{2}}{X_{\mathrm {L} }^{2}}}{\text{ is negligible for }}R\ll X_{L}.\\\gamma ={}&{\frac {V_{\mathrm {rms} }}{V_{\mathrm {DC} }}}=\left.{\frac {4V_{\mathrm {AC_{p}} }}{3{\sqrt {2}}\pi }}\cdot {\frac {R}{2\omega L}}\right/{\frac {2V_{\mathrm {AC_{p}} }}{\pi }}={\frac {R}{3{\sqrt {2}}\omega L}}.\\&{\text{Substituting }}X_{\mathrm {L} }=2\omega L,{\text{where }}L{\text{ is the inductance of the choke}};{\text{ in the more familiar form,}}\\\approx {}&0.471{\frac {R}{X_{\mathrm {L} }}},{\text{ for }}R\ll X_{L}.\end{aligned}}}
4179:
4719:{\displaystyle {\begin{aligned}V_{\mathrm {rms} }={}&{\sqrt {{\frac {1}{T}}\int _{0}^{T}\left({\frac {4V_{\mathrm {AC_{p}} }}{3\pi }}\cos(2\omega t)\right)^{2}dt}}\cdot Z_{\mathrm {RL} }\\&{\text{where }}Z_{\mathrm {RL} }{\text{ is the impedance of the RL filter formed by the choke and load}}\\={}&{\frac {4V_{\mathrm {AC_{p}} }}{3\pi }}{\sqrt {{\frac {1}{\pi }}\left_{0}^{\pi }}}\cdot {\frac {R}{\sqrt {R^{2}+X_{\mathrm {L} }^{2}}}}={\frac {4V_{\mathrm {AC_{p}} }}{3\pi }}{\sqrt {\frac {1}{2}}}\cdot {\frac {R}{\sqrt {R^{2}+X_{\mathrm {L} }^{2}}}}={\frac {4V_{\mathrm {AC_{p}} }}{3{\sqrt {2}}\pi }}\cdot {\frac {R}{X_{\mathrm {L} }}}.\end{aligned}}}
2958:
2832:
5958:
2793:
116:, the fundamental frequency can be tens of kilohertz to megahertz. The characteristics and components of ripple depend on its source: there is single-phase half- and full-wave rectification, and three-phase half- and full-wave rectification. Rectification can be controlled (uses Silicon Controlled Rectifiers (SCRs)) or uncontrolled (uses diodes). There is in addition,
5788:
5901:
non-linear characteristics of these devices, the output of a regulator is free of ripple. A simple voltage regulator may be made with a series resistor to drop voltage followed by a shunt zener diode whose Peak
Inverse Voltage (PIV) sets the maximum output voltage; if voltage rises, the diode shunts away current to maintain regulation.
474:
5556:
6066:
Power supply output requirements usually specify a minimum DC voltage, an output voltage range or percentage of voltage regulation, ripple factor. The filter must also take into account the load impedance, source voltage and voltage regulation, and power factor (i.e. for a transformer), line voltage
6024:
can be increased at the expense of increasing the ripple without increasing the order of the filter (that is, the number of components has stayed the same). On the other hand, the ripple can be reduced by increasing the order of the filter while at the same time maintaining the same rate of roll-off.
5896:
A more common solution where good ripple rejection is required is to use a reservoir capacitor to reduce the ripple to something manageable and then pass the current through a voltage regulator circuit. The regulator circuit, as well as providing a stable output voltage, will incidentally filter out
2936:
which acts as a reservoir. After a peak in output voltage the capacitor supplies the current to the load and continues to do so until the capacitor voltage has fallen to the value of the now rising next half-cycle of rectified voltage. At that point the rectifier conducts again and delivers current
2872:
Most power supplies are now switched mode designs. The filtering requirements for such power supplies are much easier to meet owing to the high frequency of the ripple waveform. The ripple frequency in switch-mode power supplies is not related to the line frequency, but is instead a multiple of the
5882:. A Π-filter results in a much lower ripple factor than a capacitor or choke input filter alone. It may be followed by additional LC or RC filter sections to further reduce ripple to a level tolerable by the load. However, use of chokes is deprecated in contemporary designs for economic reasons.
5412:
The complex impedance of a series choke is effectively part of the load impedance, so that lightly loaded circuits have increased ripple (just the opposite of a capacitor input filter). For that reason, a choke input filter is almost always part of an LC filter section, whose ripple reduction is
5948:
Ripple current results in increased dissipation in parasitic resistive portions of circuits like ESR of capacitors, DCR of transformers and inductors, internal resistance of storage batteries. The dissipation is proportional to the current squared times resistance (IR). The RMS value of ripple
5404:
Hz mains rectification. Additionally, interrupting current to an inductor will cause its magnetic flux to collapse exponentially; as current falls, a voltage spike composed of very high harmonics results which can damage other components of the power supply or circuit. This phenomenon is called
5341:
There is a minimum inductance (which is relative to the resistance of the load) required in order for a series choke to continuously conduct current. If the inductance falls below that value, current will be intermittent and output DC voltage will rise from the average input voltage to the peak
2897:
as the first component) can both reduce ripple, but have opposing effects on voltage and current, and the choice between them depends on the characteristics of the load. Capacitor input filters have poor voltage regulation, so are preferred for use in circuits with stable loads and low currents
2839:
Reducing ripple is only one of several principal considerations in power supply filter design. The filtering of ripple voltage is analogous to filtering other kinds of signals. However, in AC/DC power conversion as well as DC power generation, high voltages and currents or both may be output as
5614:
2466:
5900:
Voltage regulation is based on a different principle than filtering: it relies on the peak inverse voltage of a diode or series of diodes to set a maximum output voltage; it may also use one or more voltage amplification devices like transistors to boost voltage during sags. Because of the
3792:
2949:
is large in comparison to the period of the AC waveform, then a reasonably accurate approximation can be made by assuming that the capacitor voltage falls linearly. A further useful assumption can be made if the ripple is small compared to the DC voltage. In this case the
271:
2302:
5421:
2027:
3094:
2840:
ripple. Therefore, large discrete components like high ripple-current rated electrolytic capacitors, large iron-core chokes and wire-wound power resistors are best suited to reduce ripple to manageable proportions before passing the current to an
5919:
in power supplies, ripple voltage requires peak voltage of components to be higher; ripple current requires parasitic elements of components to be lower and dissipation capacity to be higher (components will be bigger, and quality will have to be
5944:
Ripple current is a periodic non-sinusoidal waveform derived from an AC power source characterized by high amplitude narrow bandwidth pulses. The pulses coincide with peak or near peak amplitude of an accompanying sinusoidal voltage waveform.
3929:
154:. The ripple voltage output is very large in this situation; the peak-to-peak ripple voltage is equal to the peak AC voltage minus the forward voltage of the rectifier diodes. In the case of an SS silicon diode, the forward voltage is 0.7
2611:
4166:
3337:
2771:
111:
transmission systems) may be thousands of volts. Ripple itself is a composite (non-sinusoidal) waveform consisting of harmonics of some fundamental frequency which is usually the original AC line frequency, but in the case of
5783:{\displaystyle \gamma ={\frac {V_{\mathrm {rms} }}{V_{\mathrm {DC} }}}={\frac {\left(1+{\frac {R}{R_{\mathrm {L} }}}\right)}{3{\sqrt {2}}\omega CR}}={\frac {1}{3{\sqrt {2}}\omega CR}}\approx 0.471{\frac {X_{\mathrm {C} }}{R}}}
694:
140:, the ratio of DC output power to AC input power; and form-factor, the ratio of the RMS value of the output voltage to the average value of the output voltage. Analogous ratios for output ripple current may also be computed.
123:
Various properties of ripple voltage may be important depending on application: the equation of the ripple for
Fourier analysis to determine the constituent harmonics; the peak (usually peak-to-peak) value of the voltage; the
83:. The variation may not be strictly linearly periodic. In this meaning also, ripple is usually to be considered an incidental effect, its existence being a compromise between the amount of ripple and other design parameters.
5605:
In high voltage/low current circuits, a resistor may replace the series choke in an LC filter section (creating an RC filter section). This has the effect of reducing the DC output as well as ripple. The ripple factor is
2346:
3232:
2898:(because low currents reduce ripple here). Choke input filters are preferred for circuits with variable loads and high currents (since a choke outputs a stable voltage and higher current means less ripple in this case).
3657:
5897:
nearly all of the ripple as long as the minimum level of the ripple waveform does not go below the voltage being regulated to. Switched-mode power supplies usually include a voltage regulator as part of the circuit.
256:
4773:
677:
4184:
86:
Ripple is wasted power, and has many undesirable effects in a DC circuit: it heats components, causes noise and distortion, and may cause digital circuits to operate improperly. Ripple may be reduced by an
2522:
3970:
5926:
The ripple frequency and its harmonics are within the audio band and will therefore be audible on equipment such as radio receivers, equipment for playing recordings and professional studio equipment.
534:
3550:
2844:
component like a voltage regulator, or on to the load. The kind of filtering required depends on the amplitude of the various harmonics of the ripple and the demands of the load. For example, a
3025:
3396:
469:{\displaystyle V_{\mathrm {L} }(t)={\frac {2V_{\mathrm {AC_{p}} }}{\pi }}+{\frac {4V_{\mathrm {AC_{p}} }}{\pi }}\cdot \sum _{n=1}^{\infty }{\frac {\cos(n\pi )}{1-4n^{2}}}\cdot \cos(2n\omega t)}
107:
with an alternating (AC) voltage—the ripple voltage—overlaid. The ripple component is often small in magnitude relative to the DC component, but in absolute terms, ripple (as in the case of
3647:
2696:
5551:{\displaystyle \gamma ={\frac {V_{\mathrm {rms} }}{V_{\mathrm {DC} }}}={\frac {\sqrt {2}}{3}}\cdot {\frac {1}{4\omega ^{2}CL}}\approx 0.471{\frac {X_{\mathrm {C} }}{X_{\mathrm {L} }}}}
5394:
2864:
characterized by shunt capacitors and series chokes. Series resistors may replace chokes for reducing the output DC voltage, and shunt resistors may be used for voltage regulation.
2196:
3833:
2333:
1941:
577:
3436:
3608:
3579:
3020:
2954:
through which the rectifier conducts will be small and it can be assumed that the capacitor is discharging all the way from one peak to the next with little loss of accuracy.
2160:
2064:
5846:
5598:
3164:
2649:
3262:
5932:
The presence of ripple can reduce the resolution of electronic test and measurement instruments. On an oscilloscope it will manifest itself as a visible pattern on screen.
3843:
143:
An electronic filter with high impedance at the ripple frequency may be used to reduce ripple voltage and increase or decrease DC output; such a filter is often called a
2106:
3998:
2180:
2535:
4067:
5867:
4020:
3502:
3480:
3458:
3137:
3117:
3012:
2989:
2131:
597:
5935:
Within digital circuits, it reduces the threshold, as does any form of supply rail noise, at which logic circuits give incorrect outputs and data is corrupted.
3270:
5929:
The ripple frequency is within television video bandwidth. Analogue TV receivers will exhibit a pattern of moving wavy lines if too much ripple is present.
2707:
4761:
2461:{\displaystyle FF={\frac {V_{\mathrm {L} }}{V_{\mathrm {DC} }}}={\frac {\frac {V_{\mathrm {AC_{p}} }}{\sqrt {2}}}{\frac {2V_{\mathrm {AC_{p}} }}{\pi }}}}
5875:
Similarly because of the independence of LC filter sections with respect to load, a reservoir capacitor is also commonly followed by one resulting in a
3510:
For the RMS value of the ripple voltage, the calculation is more involved as the shape of the ripple waveform has a bearing on the result. Assuming a
5406:
3787:{\displaystyle V_{\mathrm {rms} }={\frac {V_{\mathrm {pp} }}{2{\sqrt {3}}}}={\frac {I}{4{\sqrt {3}}fC}}={\frac {V_{\mathrm {DC} }}{4{\sqrt {3}}fCR}}}
3172:
6005:. The ripple of these networks, unlike regular filters, will never reach 0 dB at minimum loss if designed for optimum transmission across the
3139:
is taken from start of capacitor discharge until the minimum voltage on a full wave rectified signal as shown on the figure to the right. The time
5997:. The ripple is not usually strictly linearly periodic as can be seen from the example plot. Other examples of networks exhibiting ripple are
170:
4036:; this is a little larger than the actual value because a sawtooth wave comprises odd harmonics that aren't present in the rectified voltage.
605:
4059:
which is close to the peak input voltage. Starting with the
Fourier term for the second harmonic, and ignoring higher-order harmonics,
5923:
transformers that supply ripple current to capacitive input circuits will need to have VA ratings that exceed their load (watt) ratings
2856:, being a wholly resistive circuit, does not require any ripple filtering. Since the desired output is direct current (essentially 0
2476:
3933:
46:
after rectification. Ripple voltage originates as the output of a rectifier or from generation and commutation of DC power.
488:
5916:
ripple will cause heating in DC circuit components due to current passing through parasitic elements like ESR of capacitors
3517:
134:, the ratio of RMS value to DC voltage output; the conversion ratio (also called the rectification ratio or "efficiency")
5396:
where R is the load resistance and f the line frequency. This gives values of L = R/1131 (often stated as R/1130) for 60
5879:
3348:
2893:
A capacitor input filter (in which the first component is a shunt capacitor) and choke input filter (which has a series
2918:
3613:
2660:
2917:
dB/octave above the corner frequency. Resistive components (including resistors and parasitic elements like the
2297:{\displaystyle \gamma ={\frac {V_{\mathrm {ripple-rms} }}{V_{\mathrm {DC} }}}={\sqrt {{\frac {\pi ^{2}}{8}}-1}}}
5349:
2022:{\displaystyle V_{\text{ripple-rms}}={\frac {2V_{\mathrm {AC_{p}} }}{\pi }}{\sqrt {{\frac {\pi ^{2}}{8}}-1}}}
6096:
2922:
113:
5342:
input voltage; in effect, the inductor will behave like a capacitor. That minimum inductance, called the
3797:
2312:
57:) may also refer to the pulsed current consumption of non-linear devices like capacitor-input rectifiers.
3089:{\displaystyle {\begin{aligned}&Q=CV_{\text{pp}}\\&Q=I_{\text{ave}}t_{\text{ave}},\end{aligned}}}
6012:
The amount of ripple can be traded for other parameters in the filter design. For instance, the rate of
548:
4055:. Against this, the DC output is close to the average input voltage as opposed to the voltage with the
3409:
68:
5334:
This is a little less than 0.483 because higher-order harmonics were omitted from consideration. (See
3584:
3555:
2136:
2040:
162:
V (5R4). The output voltage is a sine wave with the negative half-cycles inverted. The equation is:
4051:. A choke has a filtering action and consequently produces a smoother waveform with fewer high-order
5819:
5571:
3924:{\displaystyle \gamma ={\frac {V_{\mathrm {rms} }}{V_{\mathrm {DC} }}}={\frac {1}{4{\sqrt {3}}fCR}}}
3142:
2961:
Ripple voltage from a full-wave rectifier, before and after the application of a smoothing capacitor
2621:
5990:
3240:
2811:
2852:
may require that ripple be reduced to no more than a few hundred nanovolts (10V). In contrast, a
6227:
5913:
ripple represents wasted power that cannot be utilized by a circuit that requires direct current
2782:
6232:
2069:
6002:
3983:
2913:
of the filter, so that a 2nd-order low-pass filter for example, reduces signal strength by 12
2874:
2606:{\displaystyle PF={\frac {V_{\mathrm {AC_{p}} }}{\frac {V_{\mathrm {AC_{p}} }}{\sqrt {2}}}}}
4161:{\displaystyle V_{\mathrm {2f} }(t)={\frac {4V_{\mathrm {AC_{p}} }}{3\pi }}\cos(2\omega t)}
117:
2165:
8:
4056:
4048:
2933:
2894:
39:
2810:
Please expand the section to include this information. Further details may exist on the
128:(RMS) value of the voltage which is a component of power transmitted; the ripple factor
6043:, the instrument of DC power generation, whose output contains a large ripple component
5998:
5982:
5978:
5852:
4005:
3487:
3465:
3443:
3122:
3102:
2997:
2974:
2841:
2116:
582:
3332:{\displaystyle V_{\text{pp}}={\frac {Q}{C}}={\frac {I_{\text{ave}}t_{\text{ave}}}{C}}}
5994:
5891:
2766:{\displaystyle TUF\approx 0.812\ ({\text{bridge}});\ 0.692\ ({\text{center-tapped}})}
92:
88:
72:
31:
6046:
5986:
5974:
5962:
2992:
2946:
2910:
144:
125:
62:
5969:
Ripple in the context of the frequency domain refers to the periodic variation in
2957:
4732:
2965:
With the above assumptions the peak-to-peak ripple voltage can be calculated as:
2861:
2853:
5909:
Ripple is undesirable in many electronic applications for a variety of reasons:
3514:
is a similar assumption to the ones above. The RMS value of a sawtooth wave is
5970:
3227:{\displaystyle t_{\text{ave}}={\frac {t_{\text{fullwave}}}{2}}={\frac {1}{2f}}}
158:
V; for vacuum tube rectifiers, forward voltage usually ranges between 25 and 67
76:
35:
6067:
variation, and any necessary filtering of source noise or harmonic distortion.
481:
Several relevant properties are apparent on inspection of the
Fourier series:
6221:
3511:
2951:
42:(AC) source. This ripple is due to incomplete suppression of the alternating
679:
is often used to represent the entire ripple voltage to simplify computation
150:
The initial step in AC to DC conversion is to send the AC current through a
2849:
2831:
103:
A non-ideal DC voltage waveform can be viewed as a composite of a constant
2969:
2845:
27:
251:{\displaystyle V_{\mathrm {L} }(t)=V_{\mathrm {AC_{p}} }\cdot |\sin(t)|}
6212:
Microwave
Filters, Impedance-Matching Networks, and Coupling Structures
5335:
672:{\displaystyle {\frac {4V_{\mathrm {AC_{p}} }}{3\pi }}\cos(2\omega t)}
6034:
4052:
151:
104:
80:
6049:, the natural response time domain analog of frequency domain ripple
4369: is the impedance of the RL filter formed by the choke and load
2932:
A common arrangement is to allow the rectifier to work into a large
75:
networks. In this case the periodic variation is a variation in the
6021:
6017:
6013:
6006:
5876:
43:
5957:
2925:
of capacitors) also reduce signal strength, but their effect is
2792:
542:
the expansion consists of only even harmonics of the fundamental
6040:
3166:
would then be equal to half the period of the full wave input.
2808:(LCL) and series resonant choke (CL) input filter topologies.
2901:
The number of reactive components in a filter is called its
5130:
5059:
2517:{\displaystyle FF={\frac {\pi }{2{\sqrt {2}}}}\approx 1.11}
108:
6037:, a non-linear device that is a principal source of ripple
3965:{\displaystyle \approx 0.453{\frac {X_{\mathrm {C} }}{R}}}
5985:. Common classes of filter which exhibit ripple are the
5949:
current can be many times the RMS of the load current.
4047:
Another approach to reducing ripple is to use a series
2905:. Each reactive component reduces signal strength by 6
2835:
Full-wave center-tapped rectifier with capacitor filter
2937:
to the reservoir until peak voltage is again reached.
2909:
dB/octave above (or below for a high-pass filter) the
529:{\displaystyle {\frac {2V_{\mathrm {AC_{p}} }}{\pi }}}
38:
within a power supply which has been derived from an
5981:
increasing insertion loss with frequency such as the
5855:
5822:
5617:
5574:
5424:
5352:
4771:
4182:
4070:
4008:
3986:
3936:
3846:
3800:
3660:
3616:
3587:
3581:
is peak voltage. With the further approximation that
3558:
3545:{\displaystyle {\frac {V_{\mathrm {p} }}{\sqrt {3}}}}
3520:
3490:
3468:
3446:
3412:
3351:
3273:
3243:
3175:
3145:
3125:
3105:
3023:
3000:
2977:
2710:
2663:
2624:
2538:
2479:
2349:
2315:
2199:
2168:
2139:
2119:
2072:
2043:
1944:
692:
608:
585:
551:
491:
274:
173:
5413:
independent of load current. The ripple factor is:
60:
As well as these time-varying phenomena, there is a
2940:
2888:
5861:
5840:
5782:
5592:
5550:
5388:
5323:
4755:
4718:
4160:
4014:
3992:
3964:
3923:
3827:
3786:
3641:
3602:
3573:
3544:
3496:
3474:
3452:
3430:
3391:{\displaystyle V_{\mathrm {pp} }={\frac {I}{2fC}}}
3390:
3331:
3256:
3226:
3158:
3131:
3111:
3088:
3006:
2983:
2765:
2690:
2643:
2605:
2516:
2460:
2327:
2296:
2174:
2154:
2125:
2100:
2058:
2021:
1927:
671:
591:
571:
545:the amplitude of the harmonics is proportional to
528:
468:
250:
4025:For the approximated formula, it is assumed that
3237:Combining the three equations above to determine
1203:
1123:
911:
885:
822:
6219:
4042:
539:the fundamental (line frequency) is not present
3642:{\displaystyle {\frac {V_{\mathrm {pp} }}{2}}}
3482:is the source (line) frequency of the AC power
3119:is the amount of charge. The current and time
2867:
2860:Hz), ripple filters are usually configured as
2066:is the time-varying voltage across the load,
5977:. Not all filters exhibit ripple, some have
5400:Hz mains rectification, and L = R/942 for 50
2691:{\displaystyle \eta \approx 0.812\ (81.2\%)}
2783:Rectifier § Rectifier output smoothing
6198:Electronic Fundamentals & Applications
6185:
6183:
5952:
263:The Fourier expansion of the function is:
5973:with frequency of a filter or some other
1235:
1148:
1008:
844:
5956:
5869:is the resistance of the filter resistor
5389:{\displaystyle L={\frac {R}{2\pi (3f)}}}
2956:
2830:
6180:
6001:networks that have been designed using
2701:The transformer utilization factor is:
602:the term for the second-order harmonic
6220:
6189:Matthaei et al., pp 120–135
1640: and substitute in terms of
16:Residual periodic variation of voltage
6097:"Capacitor Input Filter : Part3"
5885:
2877:, which is usually in the range of 50
6177:Matthaei et al., pp 85–95
5904:
5246: is the inductance of the choke
3828:{\displaystyle V_{\mathrm {DC} }=IR}
2929:, and does not vary with frequency.
2786:
2328:{\displaystyle \gamma \approx 0.483}
5801:, which makes an RC filter section
13:
6166:Principles of Television Reception
5769:
5688:
5653:
5650:
5638:
5635:
5632:
5540:
5528:
5460:
5457:
5445:
5442:
5439:
5282:
5215:
5154:
5150:
5146:
5082:
5078:
5074:
5047:
5044:
5032:
5029:
5026:
4967:
4932:
4929:
4926:
4900:
4896:
4892:
4864:
4861:
4858:
4825:
4821:
4817:
4785:
4782:
4701:
4661:
4657:
4653:
4624:
4565:
4561:
4557:
4528:
4403:
4399:
4395:
4361:
4358:
4336:
4333:
4265:
4261:
4257:
4199:
4196:
4193:
4118:
4114:
4110:
4080:
3951:
3882:
3879:
3867:
3864:
3861:
3810:
3807:
3755:
3752:
3693:
3690:
3673:
3670:
3667:
3628:
3625:
3594:
3565:
3529:
3438:is the peak-to-peak ripple voltage
3422:
3419:
3361:
3358:
2682:
2587:
2583:
2579:
2564:
2560:
2556:
2443:
2439:
2435:
2410:
2406:
2402:
2382:
2379:
2367:
2256:
2253:
2241:
2238:
2235:
2229:
2226:
2223:
2220:
2217:
2214:
2146:
2050:
1978:
1974:
1970:
1895:
1891:
1887:
1842:
1838:
1834:
1801:
1797:
1793:
1754:
1750:
1746:
1702:
1698:
1694:
1657:
1653:
1649:
1629:
1626:
1573:
1569:
1565:
1528:
1524:
1520:
1431:
1427:
1423:
1375:
1371:
1367:
1335:
1331:
1327:
1251:
1213:
1133:
1083:
1080:
1077:
1071:
1068:
1065:
1062:
1059:
1056:
1032:
1028:
1024:
946:
942:
938:
870:
866:
862:
829:
784:
781:
750:
746:
742:
725:
722:
703:
629:
625:
621:
572:{\displaystyle {\frac {1}{n^{2}}}}
512:
508:
504:
389:
356:
352:
348:
319:
315:
311:
281:
212:
208:
204:
180:
79:of the network against increasing
14:
6244:
5939:
3431:{\displaystyle V_{\mathrm {pp} }}
3342:Thus, for a full-wave rectifier:
98:
6119:Millman–Halkias, pp 112–114
5254: in the more familiar form,
3603:{\displaystyle V_{\mathrm {p} }}
3574:{\displaystyle V_{\mathrm {p} }}
2941:As a function of load resistance
2889:Capacitor vs choke input filters
2791:
2155:{\displaystyle V_{\mathrm {L} }}
2059:{\displaystyle V_{\mathrm {L} }}
768:(ignoring diode drop and losses)
6171:
4914:
4173:the ripple factor is given by:
765:
67:that arises in some classes of
6207:, McGraw-Hill Kogakusha, 1972.
6168:, p70, Pitman Publishing, 1971
6158:
6149:
6140:
6131:
6122:
6113:
6089:
6080:
6060:
5841:{\displaystyle \omega =2\pi f}
5593:{\displaystyle \omega =2\pi f}
5380:
5371:
4302:
4290:
4155:
4143:
4092:
4086:
3159:{\displaystyle t_{\text{ave}}}
2848:(MC) input circuit of a phono
2760:
2752:
2737:
2729:
2685:
2676:
2644:{\displaystyle PF={\sqrt {2}}}
2094:
2090:
2084:
2074:
1454:
1448:
1408:
1399:
1279:
1263:
1257:
1226:
1219:
1204:
1156:
1145:
1139:
1124:
1000:
994:
979:
973:
905:
899:
841:
835:
666:
654:
463:
448:
412:
403:
293:
287:
244:
240:
234:
224:
192:
186:
1:
6164:Wharton, W & Howorth, D,
6074:
4982: is negligible for
4043:As a function of series choke
4022:is the resistance of the load
3460:is the current in the circuit
3257:{\displaystyle V_{\text{pp}}}
6137:Ryder, pp 115–117
2776:
599:is the order of the harmonic
485:the constant (largest) term
114:switched-mode power supplies
7:
6155:Ryder pp 353–355
6146:Ryder pp 117–123
6028:
2868:Filtering in power supplies
10:
6249:
6200:, Pitman Publishing, 1970.
5889:
2780:
2654:The conversion ratio is:
2101:{\displaystyle |\sin(t)|}
683:The output voltages are:
6210:Matthaei, Young, Jones,
6101:www.yourelectrichome.com
6053:
5991:inverse Chebyshev filter
5961:Ripple on a fifth-order
3649:, it yields the result:
120:which uses transistors.
5953:Frequency-domain ripple
3993:{\displaystyle \gamma }
6205:Integrated Electronics
6086:Ryder, pp 107–115
5966:
5863:
5842:
5784:
5594:
5552:
5390:
5325:
4757:
4720:
4162:
4016:
3994:
3966:
3925:
3829:
3788:
3643:
3604:
3575:
3546:
3498:
3476:
3454:
3432:
3392:
3333:
3258:
3228:
3160:
3133:
3113:
3090:
3008:
2985:
2962:
2836:
2802:is missing information
2767:
2692:
2645:
2607:
2518:
2462:
2329:
2298:
2188:The ripple factor is:
2176:
2156:
2127:
2102:
2060:
2023:
1929:
673:
593:
573:
536:must be the DC voltage
530:
470:
393:
252:
91:, and eliminated by a
6003:Chebyshev polynomials
5960:
5864:
5843:
5785:
5595:
5553:
5391:
5326:
4758:
4721:
4163:
4017:
3995:
3967:
3926:
3830:
3789:
3644:
3605:
3576:
3547:
3499:
3477:
3455:
3433:
3393:
3334:
3259:
3229:
3161:
3134:
3114:
3091:
3009:
2986:
2960:
2834:
2768:
2693:
2646:
2608:
2527:The peak factor is:
2519:
2463:
2330:
2299:
2177:
2157:
2128:
2103:
2061:
2024:
1930:
674:
594:
574:
531:
471:
373:
253:
105:DC component (offset)
49:Ripple (specifically
5853:
5820:
5615:
5572:
5422:
5350:
4769:
4733:
4180:
4068:
4006:
4000:is the ripple factor
3984:
3934:
3844:
3798:
3658:
3614:
3585:
3556:
3518:
3488:
3466:
3444:
3410:
3349:
3271:
3241:
3173:
3143:
3123:
3103:
3021:
2998:
2975:
2708:
2661:
2622:
2536:
2477:
2347:
2338:The form factor is:
2313:
2197:
2175:{\displaystyle \pi }
2166:
2137:
2117:
2070:
2041:
1942:
690:
606:
583:
549:
489:
272:
171:
118:active rectification
5805:independent of load
5344:critical inductance
4977:
4942:
4874:
4634:
4538:
4497:
4238:
4057:reservoir capacitor
2934:smoothing capacitor
1813:
1766:
1714:
1540:
1488:
1387:
1347:
1202:
1122:
926:
821:
40:alternating current
5999:impedance matching
5983:Butterworth filter
5967:
5886:Voltage regulation
5859:
5838:
5780:
5590:
5548:
5386:
5321:
5319:
5206:Substituting
4961:
4920:
4852:
4716:
4714:
4618:
4522:
4434:
4224:
4158:
4012:
3990:
3962:
3921:
3825:
3784:
3639:
3600:
3571:
3542:
3504:is the capacitance
3494:
3472:
3450:
3428:
3388:
3329:
3254:
3224:
3156:
3129:
3109:
3086:
3084:
3004:
2981:
2968:The definition of
2963:
2837:
2763:
2688:
2641:
2603:
2514:
2458:
2325:
2294:
2172:
2162:, may be taken as
2152:
2123:
2098:
2056:
2019:
1925:
1923:
1787:
1740:
1688:
1514:
1361:
1321:
1313:
1188:
1108:
908:
807:
669:
589:
569:
526:
466:
248:
6214:McGraw-Hill 1964.
6203:Millman-Halkias,
6128:Ryder, p 113
5995:Elliptical filter
5905:Effects of ripple
5892:voltage regulator
5862:{\displaystyle R}
5778:
5753:
5741:
5722:
5710:
5694:
5659:
5546:
5512:
5481:
5477:
5466:
5384:
5296:
5288:
5255:
5247:
5239:
5207:
5194:
5185:
5166:
5127:
5106:
5100:
5053:
4983:
4978:
4918:
4912:
4875:
4837:
4707:
4685:
4679:
4636:
4635:
4594:
4593:
4582:
4540:
4539:
4498:
4480:
4448:
4432:
4420:
4370:
4350:
4322:
4282:
4222:
4135:
4015:{\displaystyle R}
3960:
3919:
3907:
3888:
3782:
3770:
3739:
3730:
3711:
3708:
3637:
3540:
3539:
3512:sawtooth waveform
3497:{\displaystyle C}
3475:{\displaystyle f}
3453:{\displaystyle I}
3386:
3327:
3320:
3310:
3295:
3281:
3251:
3222:
3204:
3198:
3183:
3153:
3132:{\displaystyle t}
3112:{\displaystyle Q}
3076:
3066:
3045:
3007:{\displaystyle I}
2984:{\displaystyle C}
2873:frequency of the
2829:
2828:
2758:
2751:
2745:
2735:
2728:
2675:
2639:
2601:
2600:
2599:
2506:
2503:
2456:
2455:
2423:
2422:
2388:
2292:
2284:
2262:
2133:is the period of
2126:{\displaystyle T}
2017:
2009:
1990:
1952:
1919:
1907:
1855:
1854:
1814:
1785:
1738:
1718:
1671:
1641:
1612:
1602:
1548:
1504:
1489:
1391:
1351:
1311:
1288:
1186:
1171:
1106:
1044:
957:
881:
805:
769:
763:
762:
646:
592:{\displaystyle n}
567:
524:
437:
368:
331:
93:voltage regulator
89:electronic filter
73:signal processing
34:variation of the
6240:
6190:
6187:
6178:
6175:
6169:
6162:
6156:
6153:
6147:
6144:
6138:
6135:
6129:
6126:
6120:
6117:
6111:
6110:
6108:
6107:
6093:
6087:
6084:
6068:
6064:
6047:Ringing (signal)
5987:Chebyshev filter
5975:two-port network
5965:Chebyshev filter
5868:
5866:
5865:
5860:
5847:
5845:
5844:
5839:
5789:
5787:
5786:
5781:
5779:
5774:
5773:
5772:
5762:
5754:
5752:
5742:
5737:
5728:
5723:
5721:
5711:
5706:
5700:
5696:
5695:
5693:
5692:
5691:
5678:
5665:
5660:
5658:
5657:
5656:
5643:
5642:
5641:
5625:
5599:
5597:
5596:
5591:
5557:
5555:
5554:
5549:
5547:
5545:
5544:
5543:
5533:
5532:
5531:
5521:
5513:
5511:
5504:
5503:
5487:
5482:
5473:
5472:
5467:
5465:
5464:
5463:
5450:
5449:
5448:
5432:
5403:
5399:
5395:
5393:
5392:
5387:
5385:
5383:
5360:
5330:
5328:
5327:
5322:
5320:
5313:
5312:
5297:
5294:
5289:
5287:
5286:
5285:
5272:
5265:
5256:
5253:
5248:
5245:
5240:
5237:
5220:
5219:
5218:
5208:
5205:
5202:
5195:
5193:
5186:
5181:
5172:
5167:
5162:
5161:
5160:
5159:
5158:
5157:
5135:
5133:
5129:
5128:
5126:
5112:
5107:
5105:
5101:
5096:
5090:
5089:
5088:
5087:
5086:
5085:
5063:
5054:
5052:
5051:
5050:
5037:
5036:
5035:
5019:
5015:
5000:
4999:
4984:
4981:
4979:
4976:
4971:
4970:
4960:
4959:
4950:
4941:
4936:
4935:
4919:
4916:
4913:
4908:
4907:
4906:
4905:
4904:
4903:
4881:
4876:
4873:
4868:
4867:
4848:
4847:
4842:
4838:
4833:
4832:
4831:
4830:
4829:
4828:
4806:
4799:
4795:
4790:
4789:
4788:
4762:
4760:
4759:
4754:
4750:
4749:
4725:
4723:
4722:
4717:
4715:
4708:
4706:
4705:
4704:
4691:
4686:
4684:
4680:
4675:
4669:
4668:
4667:
4666:
4665:
4664:
4642:
4637:
4633:
4628:
4627:
4614:
4613:
4604:
4600:
4595:
4586:
4585:
4583:
4581:
4573:
4572:
4571:
4570:
4569:
4568:
4546:
4541:
4537:
4532:
4531:
4518:
4517:
4508:
4504:
4499:
4496:
4491:
4486:
4482:
4481:
4479:
4471:
4454:
4449:
4441:
4433:
4425:
4423:
4421:
4419:
4411:
4410:
4409:
4408:
4407:
4406:
4384:
4380:
4371:
4368:
4366:
4365:
4364:
4351:
4348:
4345:
4341:
4340:
4339:
4323:
4315:
4314:
4309:
4305:
4283:
4281:
4273:
4272:
4271:
4270:
4269:
4268:
4246:
4237:
4232:
4223:
4215:
4213:
4209:
4204:
4203:
4202:
4167:
4165:
4164:
4159:
4136:
4134:
4126:
4125:
4124:
4123:
4122:
4121:
4099:
4085:
4084:
4083:
4021:
4019:
4018:
4013:
3999:
3997:
3996:
3991:
3971:
3969:
3968:
3963:
3961:
3956:
3955:
3954:
3944:
3930:
3928:
3927:
3922:
3920:
3918:
3908:
3903:
3894:
3889:
3887:
3886:
3885:
3872:
3871:
3870:
3854:
3834:
3832:
3831:
3826:
3815:
3814:
3813:
3793:
3791:
3790:
3785:
3783:
3781:
3771:
3766:
3760:
3759:
3758:
3745:
3740:
3738:
3731:
3726:
3717:
3712:
3710:
3709:
3704:
3698:
3697:
3696:
3683:
3678:
3677:
3676:
3648:
3646:
3645:
3640:
3638:
3633:
3632:
3631:
3618:
3609:
3607:
3606:
3601:
3599:
3598:
3597:
3580:
3578:
3577:
3572:
3570:
3569:
3568:
3551:
3549:
3548:
3543:
3541:
3535:
3534:
3533:
3532:
3522:
3503:
3501:
3500:
3495:
3481:
3479:
3478:
3473:
3459:
3457:
3456:
3451:
3437:
3435:
3434:
3429:
3427:
3426:
3425:
3397:
3395:
3394:
3389:
3387:
3385:
3371:
3366:
3365:
3364:
3338:
3336:
3335:
3330:
3328:
3323:
3322:
3321:
3318:
3312:
3311:
3308:
3301:
3296:
3288:
3283:
3282:
3279:
3263:
3261:
3260:
3255:
3253:
3252:
3249:
3233:
3231:
3230:
3225:
3223:
3221:
3210:
3205:
3200:
3199:
3196:
3190:
3185:
3184:
3181:
3165:
3163:
3162:
3157:
3155:
3154:
3151:
3138:
3136:
3135:
3130:
3118:
3116:
3115:
3110:
3095:
3093:
3092:
3087:
3085:
3078:
3077:
3074:
3068:
3067:
3064:
3051:
3047:
3046:
3043:
3027:
3013:
3011:
3010:
3005:
2990:
2988:
2987:
2982:
2947:RC time constant
2916:
2911:corner frequency
2908:
2884:
2880:
2862:low pass filters
2859:
2824:
2821:
2815:
2795:
2787:
2772:
2770:
2769:
2764:
2759:
2756:
2749:
2743:
2736:
2733:
2726:
2697:
2695:
2694:
2689:
2673:
2650:
2648:
2647:
2642:
2640:
2635:
2612:
2610:
2609:
2604:
2602:
2595:
2594:
2593:
2592:
2591:
2590:
2572:
2571:
2570:
2569:
2568:
2567:
2549:
2523:
2521:
2520:
2515:
2507:
2505:
2504:
2499:
2490:
2467:
2465:
2464:
2459:
2457:
2451:
2450:
2449:
2448:
2447:
2446:
2424:
2418:
2417:
2416:
2415:
2414:
2413:
2395:
2394:
2389:
2387:
2386:
2385:
2372:
2371:
2370:
2360:
2334:
2332:
2331:
2326:
2303:
2301:
2300:
2295:
2293:
2285:
2280:
2279:
2270:
2268:
2263:
2261:
2260:
2259:
2246:
2245:
2244:
2207:
2181:
2179:
2178:
2173:
2161:
2159:
2158:
2153:
2151:
2150:
2149:
2132:
2130:
2129:
2124:
2108:for period 0 to
2107:
2105:
2104:
2099:
2097:
2077:
2065:
2063:
2062:
2057:
2055:
2054:
2053:
2028:
2026:
2025:
2020:
2018:
2010:
2005:
2004:
1995:
1993:
1991:
1986:
1985:
1984:
1983:
1982:
1981:
1959:
1954:
1953:
1950:
1934:
1932:
1931:
1926:
1924:
1920:
1918:
1917:
1912:
1908:
1903:
1902:
1901:
1900:
1899:
1898:
1876:
1866:
1865:
1860:
1856:
1850:
1849:
1848:
1847:
1846:
1845:
1827:
1820:
1815:
1812:
1807:
1806:
1805:
1804:
1786:
1784:
1783:
1771:
1765:
1760:
1759:
1758:
1757:
1739:
1737:
1736:
1724:
1719:
1713:
1708:
1707:
1706:
1705:
1687:
1685:
1681:
1672:
1669:
1664:
1663:
1662:
1661:
1660:
1642:
1639:
1634:
1633:
1632:
1613:
1610:
1607:
1603:
1601:
1597:
1593:
1592:
1580:
1579:
1578:
1577:
1576:
1549:
1544:
1539:
1534:
1533:
1532:
1531:
1512:
1505:
1497:
1495:
1490:
1487:
1482:
1477:
1473:
1469:
1468:
1438:
1437:
1436:
1435:
1434:
1392:
1386:
1381:
1380:
1379:
1378:
1360:
1352:
1346:
1341:
1340:
1339:
1338:
1320:
1312:
1304:
1302:
1298:
1289:
1278:
1277:
1256:
1255:
1254:
1234:
1233:
1218:
1217:
1216:
1201:
1196:
1187:
1179:
1177:
1172:
1164:
1163:
1138:
1137:
1136:
1121:
1116:
1107:
1099:
1097:
1093:
1088:
1087:
1086:
1045:
1040:
1039:
1038:
1037:
1036:
1035:
1013:
1007:
1003:
958:
953:
952:
951:
950:
949:
931:
925:
920:
915:
914:
889:
888:
882:
877:
876:
875:
874:
873:
855:
834:
833:
832:
820:
815:
806:
798:
794:
789:
788:
787:
770:
767:
764:
758:
757:
756:
755:
754:
753:
735:
730:
729:
728:
713:
708:
707:
706:
678:
676:
675:
670:
647:
645:
637:
636:
635:
634:
633:
632:
610:
598:
596:
595:
590:
578:
576:
575:
570:
568:
566:
565:
553:
535:
533:
532:
527:
525:
520:
519:
518:
517:
516:
515:
493:
475:
473:
472:
467:
438:
436:
435:
434:
415:
395:
392:
387:
369:
364:
363:
362:
361:
360:
359:
337:
332:
327:
326:
325:
324:
323:
322:
300:
286:
285:
284:
257:
255:
254:
249:
247:
227:
219:
218:
217:
216:
215:
185:
184:
183:
161:
157:
145:smoothing filter
126:root mean square
63:frequency domain
30:is the residual
6248:
6247:
6243:
6242:
6241:
6239:
6238:
6237:
6218:
6217:
6193:
6188:
6181:
6176:
6172:
6163:
6159:
6154:
6150:
6145:
6141:
6136:
6132:
6127:
6123:
6118:
6114:
6105:
6103:
6095:
6094:
6090:
6085:
6081:
6077:
6072:
6071:
6065:
6061:
6056:
6031:
5955:
5942:
5907:
5894:
5888:
5854:
5851:
5850:
5821:
5818:
5817:
5796:
5768:
5767:
5763:
5761:
5736:
5732:
5727:
5705:
5701:
5687:
5686:
5682:
5677:
5670:
5666:
5664:
5649:
5648:
5644:
5631:
5630:
5626:
5624:
5616:
5613:
5612:
5573:
5570:
5569:
5539:
5538:
5534:
5527:
5526:
5522:
5520:
5499:
5495:
5491:
5486:
5471:
5456:
5455:
5451:
5438:
5437:
5433:
5431:
5423:
5420:
5419:
5407:flyback voltage
5401:
5397:
5364:
5359:
5351:
5348:
5347:
5318:
5317:
5308:
5304:
5295: for
5293:
5281:
5280:
5276:
5271:
5266:
5264:
5258:
5257:
5252:
5244:
5236:
5214:
5213:
5209:
5204:
5200:
5199:
5180:
5176:
5171:
5153:
5149:
5145:
5144:
5140:
5136:
5134:
5116:
5111:
5095:
5091:
5081:
5077:
5073:
5072:
5068:
5064:
5062:
5061:
5058:
5043:
5042:
5038:
5025:
5024:
5020:
5018:
5016:
5014:
5005:
5004:
4995:
4991:
4980:
4972:
4966:
4965:
4955:
4951:
4949:
4937:
4925:
4924:
4915:
4899:
4895:
4891:
4890:
4886:
4882:
4880:
4869:
4857:
4856:
4843:
4824:
4820:
4816:
4815:
4811:
4807:
4805:
4801:
4800:
4798:
4796:
4794:
4781:
4780:
4776:
4772:
4770:
4767:
4766:
4745:
4741:
4734:
4731:
4730:
4713:
4712:
4700:
4699:
4695:
4690:
4674:
4670:
4660:
4656:
4652:
4651:
4647:
4643:
4641:
4629:
4623:
4622:
4609:
4605:
4599:
4584:
4574:
4564:
4560:
4556:
4555:
4551:
4547:
4545:
4533:
4527:
4526:
4513:
4509:
4503:
4492:
4487:
4472:
4455:
4453:
4440:
4439:
4435:
4424:
4422:
4412:
4402:
4398:
4394:
4393:
4389:
4385:
4383:
4381:
4379:
4373:
4372:
4367:
4357:
4356:
4352:
4347:
4343:
4342:
4332:
4331:
4327:
4310:
4274:
4264:
4260:
4256:
4255:
4251:
4247:
4245:
4244:
4240:
4239:
4233:
4228:
4214:
4212:
4210:
4208:
4192:
4191:
4187:
4183:
4181:
4178:
4177:
4127:
4117:
4113:
4109:
4108:
4104:
4100:
4098:
4076:
4075:
4071:
4069:
4066:
4065:
4045:
4031:
4007:
4004:
4003:
3985:
3982:
3981:
3973:
3950:
3949:
3945:
3943:
3935:
3932:
3931:
3902:
3898:
3893:
3878:
3877:
3873:
3860:
3859:
3855:
3853:
3845:
3842:
3841:
3806:
3805:
3801:
3799:
3796:
3795:
3765:
3761:
3751:
3750:
3746:
3744:
3725:
3721:
3716:
3703:
3699:
3689:
3688:
3684:
3682:
3666:
3665:
3661:
3659:
3656:
3655:
3624:
3623:
3619:
3617:
3615:
3612:
3611:
3593:
3592:
3588:
3586:
3583:
3582:
3564:
3563:
3559:
3557:
3554:
3553:
3528:
3527:
3523:
3521:
3519:
3516:
3515:
3489:
3486:
3485:
3467:
3464:
3463:
3445:
3442:
3441:
3418:
3417:
3413:
3411:
3408:
3407:
3399:
3375:
3370:
3357:
3356:
3352:
3350:
3347:
3346:
3317:
3313:
3307:
3303:
3302:
3300:
3287:
3278:
3274:
3272:
3269:
3268:
3248:
3244:
3242:
3239:
3238:
3214:
3209:
3195:
3191:
3189:
3180:
3176:
3174:
3171:
3170:
3150:
3146:
3144:
3141:
3140:
3124:
3121:
3120:
3104:
3101:
3100:
3083:
3082:
3073:
3069:
3063:
3059:
3049:
3048:
3042:
3038:
3024:
3022:
3019:
3018:
2999:
2996:
2995:
2976:
2973:
2972:
2943:
2914:
2906:
2891:
2882:
2878:
2875:chopper circuit
2870:
2857:
2854:battery charger
2825:
2819:
2816:
2809:
2796:
2785:
2779:
2774:
2755:
2732:
2709:
2706:
2705:
2699:
2662:
2659:
2658:
2652:
2634:
2623:
2620:
2619:
2586:
2582:
2578:
2577:
2573:
2563:
2559:
2555:
2554:
2550:
2548:
2537:
2534:
2533:
2525:
2498:
2494:
2489:
2478:
2475:
2474:
2442:
2438:
2434:
2433:
2429:
2425:
2409:
2405:
2401:
2400:
2396:
2393:
2378:
2377:
2373:
2366:
2365:
2361:
2359:
2348:
2345:
2344:
2336:
2314:
2311:
2310:
2275:
2271:
2269:
2267:
2252:
2251:
2247:
2213:
2212:
2208:
2206:
2198:
2195:
2194:
2167:
2164:
2163:
2145:
2144:
2140:
2138:
2135:
2134:
2118:
2115:
2114:
2093:
2073:
2071:
2068:
2067:
2049:
2048:
2044:
2042:
2039:
2038:
2030:
2000:
1996:
1994:
1992:
1977:
1973:
1969:
1968:
1964:
1960:
1958:
1949:
1945:
1943:
1940:
1939:
1922:
1921:
1913:
1894:
1890:
1886:
1885:
1881:
1877:
1875:
1871:
1870:
1861:
1841:
1837:
1833:
1832:
1828:
1826:
1822:
1821:
1819:
1808:
1800:
1796:
1792:
1791:
1779:
1775:
1770:
1761:
1753:
1749:
1745:
1744:
1732:
1728:
1723:
1709:
1701:
1697:
1693:
1692:
1686:
1684:
1682:
1680:
1674:
1673:
1668:
1656:
1652:
1648:
1647:
1643:
1638:
1625:
1624:
1620:
1609:
1605:
1604:
1588:
1584:
1572:
1568:
1564:
1563:
1559:
1535:
1527:
1523:
1519:
1518:
1513:
1511:
1510:
1506:
1496:
1494:
1483:
1478:
1464:
1460:
1430:
1426:
1422:
1421:
1417:
1382:
1374:
1370:
1366:
1365:
1359:
1342:
1334:
1330:
1326:
1325:
1319:
1318:
1314:
1303:
1301:
1299:
1297:
1291:
1290:
1273:
1269:
1250:
1249:
1245:
1229:
1225:
1212:
1211:
1207:
1197:
1192:
1178:
1176:
1159:
1155:
1132:
1131:
1127:
1117:
1112:
1098:
1096:
1094:
1092:
1055:
1054:
1050:
1047:
1046:
1031:
1027:
1023:
1022:
1018:
1014:
1012:
963:
959:
945:
941:
937:
936:
932:
930:
921:
916:
910:
909:
884:
883:
869:
865:
861:
860:
856:
854:
828:
827:
823:
816:
811:
797:
795:
793:
780:
779:
775:
772:
771:
766:
749:
745:
741:
740:
736:
734:
721:
720:
716:
714:
712:
702:
701:
697:
693:
691:
688:
687:
638:
628:
624:
620:
619:
615:
611:
609:
607:
604:
603:
584:
581:
580:
561:
557:
552:
550:
547:
546:
511:
507:
503:
502:
498:
494:
492:
490:
487:
486:
430:
426:
416:
396:
394:
388:
377:
355:
351:
347:
346:
342:
338:
336:
318:
314:
310:
309:
305:
301:
299:
280:
279:
275:
273:
270:
269:
243:
223:
211:
207:
203:
202:
198:
179:
178:
174:
172:
169:
168:
159:
155:
139:
133:
101:
17:
12:
11:
5:
6246:
6236:
6235:
6230:
6228:Electric power
6216:
6215:
6208:
6201:
6192:
6191:
6179:
6170:
6157:
6148:
6139:
6130:
6121:
6112:
6088:
6078:
6076:
6073:
6070:
6069:
6058:
6057:
6055:
6052:
6051:
6050:
6044:
6038:
6030:
6027:
5971:insertion loss
5954:
5951:
5941:
5940:Ripple current
5938:
5937:
5936:
5933:
5930:
5927:
5924:
5921:
5917:
5914:
5906:
5903:
5890:Main article:
5887:
5884:
5873:
5872:
5871:
5870:
5858:
5848:
5837:
5834:
5831:
5828:
5825:
5809:
5808:
5807:
5806:
5794:
5777:
5771:
5766:
5760:
5757:
5751:
5748:
5745:
5740:
5735:
5731:
5726:
5720:
5717:
5714:
5709:
5704:
5699:
5690:
5685:
5681:
5676:
5673:
5669:
5663:
5655:
5652:
5647:
5640:
5637:
5634:
5629:
5623:
5620:
5603:
5602:
5601:
5600:
5589:
5586:
5583:
5580:
5577:
5561:
5560:
5559:
5558:
5542:
5537:
5530:
5525:
5519:
5516:
5510:
5507:
5502:
5498:
5494:
5490:
5485:
5480:
5476:
5470:
5462:
5459:
5454:
5447:
5444:
5441:
5436:
5430:
5427:
5382:
5379:
5376:
5373:
5370:
5367:
5363:
5358:
5355:
5332:
5331:
5316:
5311:
5307:
5303:
5300:
5292:
5284:
5279:
5275:
5270:
5267:
5263:
5260:
5259:
5251:
5243:
5235:
5232:
5229:
5226:
5223:
5217:
5212:
5203:
5201:
5198:
5192:
5189:
5184:
5179:
5175:
5170:
5165:
5156:
5152:
5148:
5143:
5139:
5132:
5125:
5122:
5119:
5115:
5110:
5104:
5099:
5094:
5084:
5080:
5076:
5071:
5067:
5060:
5057:
5049:
5046:
5041:
5034:
5031:
5028:
5023:
5017:
5013:
5010:
5007:
5006:
5003:
4998:
4994:
4990:
4987:
4975:
4969:
4964:
4958:
4954:
4948:
4945:
4940:
4934:
4931:
4928:
4923:
4911:
4902:
4898:
4894:
4889:
4885:
4879:
4872:
4866:
4863:
4860:
4855:
4851:
4846:
4841:
4836:
4827:
4823:
4819:
4814:
4810:
4804:
4797:
4793:
4787:
4784:
4779:
4775:
4774:
4753:
4748:
4744:
4740:
4737:
4727:
4726:
4711:
4703:
4698:
4694:
4689:
4683:
4678:
4673:
4663:
4659:
4655:
4650:
4646:
4640:
4632:
4626:
4621:
4617:
4612:
4608:
4603:
4598:
4592:
4589:
4580:
4577:
4567:
4563:
4559:
4554:
4550:
4544:
4536:
4530:
4525:
4521:
4516:
4512:
4507:
4502:
4495:
4490:
4485:
4478:
4475:
4470:
4467:
4464:
4461:
4458:
4452:
4447:
4444:
4438:
4431:
4428:
4418:
4415:
4405:
4401:
4397:
4392:
4388:
4382:
4378:
4375:
4374:
4363:
4360:
4355:
4346:
4344:
4338:
4335:
4330:
4326:
4321:
4318:
4313:
4308:
4304:
4301:
4298:
4295:
4292:
4289:
4286:
4280:
4277:
4267:
4263:
4259:
4254:
4250:
4243:
4236:
4231:
4227:
4221:
4218:
4211:
4207:
4201:
4198:
4195:
4190:
4186:
4185:
4171:
4170:
4169:
4168:
4157:
4154:
4151:
4148:
4145:
4142:
4139:
4133:
4130:
4120:
4116:
4112:
4107:
4103:
4097:
4094:
4091:
4088:
4082:
4079:
4074:
4044:
4041:
4040:
4039:
4038:
4037:
4029:
4023:
4011:
4001:
3989:
3959:
3953:
3948:
3942:
3939:
3917:
3914:
3911:
3906:
3901:
3897:
3892:
3884:
3881:
3876:
3869:
3866:
3863:
3858:
3852:
3849:
3839:
3838:
3837:
3836:
3835:
3824:
3821:
3818:
3812:
3809:
3804:
3780:
3777:
3774:
3769:
3764:
3757:
3754:
3749:
3743:
3737:
3734:
3729:
3724:
3720:
3715:
3707:
3702:
3695:
3692:
3687:
3681:
3675:
3672:
3669:
3664:
3636:
3630:
3627:
3622:
3596:
3591:
3567:
3562:
3538:
3531:
3526:
3508:
3507:
3506:
3505:
3493:
3483:
3471:
3461:
3449:
3439:
3424:
3421:
3416:
3384:
3381:
3378:
3374:
3369:
3363:
3360:
3355:
3344:
3340:
3339:
3326:
3316:
3306:
3299:
3294:
3291:
3286:
3277:
3247:
3235:
3234:
3220:
3217:
3213:
3208:
3203:
3194:
3188:
3179:
3149:
3128:
3108:
3097:
3096:
3081:
3072:
3062:
3058:
3055:
3052:
3050:
3041:
3037:
3034:
3031:
3028:
3026:
3003:
2980:
2942:
2939:
2921:of chokes and
2890:
2887:
2869:
2866:
2827:
2826:
2799:
2797:
2790:
2778:
2775:
2762:
2754:
2748:
2742:
2739:
2731:
2725:
2722:
2719:
2716:
2713:
2703:
2687:
2684:
2681:
2678:
2672:
2669:
2666:
2656:
2638:
2633:
2630:
2627:
2617:
2616:
2615:
2614:
2613:
2598:
2589:
2585:
2581:
2576:
2566:
2562:
2558:
2553:
2547:
2544:
2541:
2513:
2510:
2502:
2497:
2493:
2488:
2485:
2482:
2472:
2471:
2470:
2469:
2468:
2454:
2445:
2441:
2437:
2432:
2428:
2421:
2412:
2408:
2404:
2399:
2392:
2384:
2381:
2376:
2369:
2364:
2358:
2355:
2352:
2324:
2321:
2318:
2308:
2307:
2306:
2305:
2304:
2291:
2288:
2283:
2278:
2274:
2266:
2258:
2255:
2250:
2243:
2240:
2237:
2234:
2231:
2228:
2225:
2222:
2219:
2216:
2211:
2205:
2202:
2186:
2185:
2184:
2183:
2171:
2148:
2143:
2122:
2112:
2096:
2092:
2089:
2086:
2083:
2080:
2076:
2052:
2047:
2016:
2013:
2008:
2003:
1999:
1989:
1980:
1976:
1972:
1967:
1963:
1957:
1948:
1937:
1936:
1935:
1916:
1911:
1906:
1897:
1893:
1889:
1884:
1880:
1874:
1869:
1864:
1859:
1853:
1844:
1840:
1836:
1831:
1825:
1818:
1811:
1803:
1799:
1795:
1790:
1782:
1778:
1774:
1769:
1764:
1756:
1752:
1748:
1743:
1735:
1731:
1727:
1722:
1717:
1712:
1704:
1700:
1696:
1691:
1683:
1679:
1676:
1675:
1667:
1659:
1655:
1651:
1646:
1637:
1631:
1628:
1623:
1619:
1616:
1608:
1606:
1600:
1596:
1591:
1587:
1583:
1575:
1571:
1567:
1562:
1558:
1555:
1552:
1547:
1543:
1538:
1530:
1526:
1522:
1517:
1509:
1503:
1500:
1493:
1486:
1481:
1476:
1472:
1467:
1463:
1459:
1456:
1453:
1450:
1447:
1444:
1441:
1433:
1429:
1425:
1420:
1416:
1413:
1410:
1407:
1404:
1401:
1398:
1395:
1390:
1385:
1377:
1373:
1369:
1364:
1358:
1355:
1350:
1345:
1337:
1333:
1329:
1324:
1317:
1310:
1307:
1300:
1296:
1293:
1292:
1287:
1284:
1281:
1276:
1272:
1268:
1265:
1262:
1259:
1253:
1248:
1244:
1241:
1238:
1232:
1228:
1224:
1221:
1215:
1210:
1206:
1200:
1195:
1191:
1185:
1182:
1175:
1170:
1167:
1162:
1158:
1154:
1151:
1147:
1144:
1141:
1135:
1130:
1126:
1120:
1115:
1111:
1105:
1102:
1095:
1091:
1085:
1082:
1079:
1076:
1073:
1070:
1067:
1064:
1061:
1058:
1053:
1049:
1048:
1043:
1034:
1030:
1026:
1021:
1017:
1011:
1006:
1002:
999:
996:
993:
990:
987:
984:
981:
978:
975:
972:
969:
966:
962:
956:
948:
944:
940:
935:
929:
924:
919:
913:
907:
904:
901:
898:
895:
892:
887:
880:
872:
868:
864:
859:
853:
850:
847:
843:
840:
837:
831:
826:
819:
814:
810:
804:
801:
796:
792:
786:
783:
778:
774:
773:
761:
752:
748:
744:
739:
733:
727:
724:
719:
715:
711:
705:
700:
696:
695:
681:
680:
668:
665:
662:
659:
656:
653:
650:
644:
641:
631:
627:
623:
618:
614:
600:
588:
564:
560:
556:
543:
540:
537:
523:
514:
510:
506:
501:
497:
479:
478:
477:
476:
465:
462:
459:
456:
453:
450:
447:
444:
441:
433:
429:
425:
422:
419:
414:
411:
408:
405:
402:
399:
391:
386:
383:
380:
376:
372:
367:
358:
354:
350:
345:
341:
335:
330:
321:
317:
313:
308:
304:
298:
295:
292:
289:
283:
278:
261:
260:
259:
258:
246:
242:
239:
236:
233:
230:
226:
222:
214:
210:
206:
201:
197:
194:
191:
188:
182:
177:
135:
129:
100:
99:Voltage ripple
97:
77:insertion loss
51:ripple current
24:ripple voltage
22:(specifically
15:
9:
6:
4:
3:
2:
6245:
6234:
6233:Filter theory
6231:
6229:
6226:
6225:
6223:
6213:
6209:
6206:
6202:
6199:
6195:
6194:
6186:
6184:
6174:
6167:
6161:
6152:
6143:
6134:
6125:
6116:
6102:
6098:
6092:
6083:
6079:
6063:
6059:
6048:
6045:
6042:
6039:
6036:
6033:
6032:
6026:
6023:
6019:
6015:
6010:
6008:
6004:
6000:
5996:
5992:
5988:
5984:
5980:
5979:monotonically
5976:
5972:
5964:
5959:
5950:
5946:
5934:
5931:
5928:
5925:
5922:
5918:
5915:
5912:
5911:
5910:
5902:
5898:
5893:
5883:
5881:
5878:
5856:
5849:
5835:
5832:
5829:
5826:
5823:
5816:
5815:
5814:
5813:
5812:
5804:
5800:
5793:
5775:
5764:
5758:
5755:
5749:
5746:
5743:
5738:
5733:
5729:
5724:
5718:
5715:
5712:
5707:
5702:
5697:
5683:
5679:
5674:
5671:
5667:
5661:
5645:
5627:
5621:
5618:
5611:
5610:
5609:
5608:
5607:
5587:
5584:
5581:
5578:
5575:
5568:
5567:
5566:
5565:
5564:
5535:
5523:
5517:
5514:
5508:
5505:
5500:
5496:
5492:
5488:
5483:
5478:
5474:
5468:
5452:
5434:
5428:
5425:
5418:
5417:
5416:
5415:
5414:
5410:
5408:
5377:
5374:
5368:
5365:
5361:
5356:
5353:
5345:
5339:
5337:
5314:
5309:
5305:
5301:
5298:
5290:
5277:
5273:
5268:
5261:
5249:
5241:
5233:
5230:
5227:
5224:
5221:
5210:
5196:
5190:
5187:
5182:
5177:
5173:
5168:
5163:
5141:
5137:
5123:
5120:
5117:
5113:
5108:
5102:
5097:
5092:
5069:
5065:
5055:
5039:
5021:
5011:
5008:
5001:
4996:
4992:
4988:
4985:
4973:
4962:
4956:
4952:
4946:
4943:
4938:
4921:
4917:because
4909:
4887:
4883:
4877:
4870:
4853:
4849:
4844:
4839:
4834:
4812:
4808:
4802:
4791:
4777:
4765:
4764:
4763:
4751:
4746:
4742:
4738:
4735:
4709:
4696:
4692:
4687:
4681:
4676:
4671:
4648:
4644:
4638:
4630:
4619:
4615:
4610:
4606:
4601:
4596:
4590:
4587:
4578:
4575:
4552:
4548:
4542:
4534:
4523:
4519:
4514:
4510:
4505:
4500:
4493:
4488:
4483:
4476:
4473:
4468:
4465:
4462:
4459:
4456:
4450:
4445:
4442:
4436:
4429:
4426:
4416:
4413:
4390:
4386:
4376:
4353:
4328:
4324:
4319:
4316:
4311:
4306:
4299:
4296:
4293:
4287:
4284:
4278:
4275:
4252:
4248:
4241:
4234:
4229:
4225:
4219:
4216:
4205:
4188:
4176:
4175:
4174:
4152:
4149:
4146:
4140:
4137:
4131:
4128:
4105:
4101:
4095:
4089:
4077:
4072:
4064:
4063:
4062:
4061:
4060:
4058:
4054:
4050:
4035:
4028:
4024:
4009:
4002:
3987:
3980:
3979:
3978:
3977:
3976:
3972:
3957:
3946:
3940:
3937:
3915:
3912:
3909:
3904:
3899:
3895:
3890:
3874:
3856:
3850:
3847:
3822:
3819:
3816:
3802:
3778:
3775:
3772:
3767:
3762:
3747:
3741:
3735:
3732:
3727:
3722:
3718:
3713:
3705:
3700:
3685:
3679:
3662:
3654:
3653:
3652:
3651:
3650:
3634:
3620:
3589:
3560:
3536:
3524:
3513:
3491:
3484:
3469:
3462:
3447:
3440:
3414:
3406:
3405:
3404:
3403:
3402:
3398:
3382:
3379:
3376:
3372:
3367:
3353:
3343:
3324:
3314:
3304:
3297:
3292:
3289:
3284:
3275:
3267:
3266:
3265:
3245:
3218:
3215:
3211:
3206:
3201:
3192:
3186:
3177:
3169:
3168:
3167:
3147:
3126:
3106:
3079:
3070:
3060:
3056:
3053:
3039:
3035:
3032:
3029:
3017:
3016:
3015:
3001:
2994:
2978:
2971:
2966:
2959:
2955:
2953:
2948:
2938:
2935:
2930:
2928:
2924:
2920:
2912:
2904:
2899:
2896:
2886:
2876:
2865:
2863:
2855:
2851:
2847:
2843:
2833:
2823:
2820:November 2017
2813:
2807:
2803:
2800:This section
2798:
2794:
2789:
2788:
2784:
2773:
2757:center-tapped
2746:
2740:
2723:
2720:
2717:
2714:
2711:
2702:
2698:
2679:
2670:
2667:
2664:
2655:
2651:
2636:
2631:
2628:
2625:
2596:
2574:
2551:
2545:
2542:
2539:
2532:
2531:
2530:
2529:
2528:
2524:
2511:
2508:
2500:
2495:
2491:
2486:
2483:
2480:
2452:
2430:
2426:
2419:
2397:
2390:
2374:
2362:
2356:
2353:
2350:
2343:
2342:
2341:
2340:
2339:
2335:
2322:
2319:
2316:
2289:
2286:
2281:
2276:
2272:
2264:
2248:
2232:
2209:
2203:
2200:
2193:
2192:
2191:
2190:
2189:
2169:
2141:
2120:
2113:
2111:
2087:
2081:
2078:
2045:
2037:
2036:
2035:
2034:
2033:
2029:
2014:
2011:
2006:
2001:
1997:
1987:
1965:
1961:
1955:
1946:
1914:
1909:
1904:
1882:
1878:
1872:
1867:
1862:
1857:
1851:
1829:
1823:
1816:
1809:
1788:
1780:
1776:
1772:
1767:
1762:
1741:
1733:
1729:
1725:
1720:
1715:
1710:
1689:
1677:
1665:
1644:
1635:
1621:
1617:
1614:
1598:
1594:
1589:
1585:
1581:
1560:
1556:
1553:
1550:
1545:
1541:
1536:
1515:
1507:
1501:
1498:
1491:
1484:
1479:
1474:
1470:
1465:
1461:
1457:
1451:
1445:
1442:
1439:
1418:
1414:
1411:
1405:
1402:
1396:
1393:
1388:
1383:
1362:
1356:
1353:
1348:
1343:
1322:
1315:
1308:
1305:
1294:
1285:
1282:
1274:
1270:
1266:
1260:
1246:
1242:
1239:
1236:
1230:
1222:
1208:
1198:
1193:
1189:
1183:
1180:
1173:
1168:
1165:
1160:
1152:
1149:
1142:
1128:
1118:
1113:
1109:
1103:
1100:
1089:
1074:
1051:
1041:
1019:
1015:
1009:
1004:
997:
991:
988:
985:
982:
976:
970:
967:
964:
960:
954:
933:
927:
922:
917:
902:
896:
893:
890:
878:
857:
851:
848:
845:
838:
824:
817:
812:
808:
802:
799:
790:
776:
759:
737:
731:
717:
709:
698:
686:
685:
684:
663:
660:
657:
651:
648:
642:
639:
616:
612:
601:
586:
562:
558:
554:
544:
541:
538:
521:
499:
495:
484:
483:
482:
460:
457:
454:
451:
445:
442:
439:
431:
427:
423:
420:
417:
409:
406:
400:
397:
384:
381:
378:
374:
370:
365:
343:
339:
333:
328:
306:
302:
296:
290:
276:
268:
267:
266:
265:
264:
237:
231:
228:
220:
199:
195:
189:
175:
167:
166:
165:
164:
163:
153:
148:
146:
141:
138:
132:
127:
121:
119:
115:
110:
106:
96:
94:
90:
84:
82:
78:
74:
70:
66:
64:
58:
56:
55:surge current
52:
47:
45:
41:
37:
33:
29:
25:
21:
6211:
6204:
6197:
6196:Ryder, J D,
6173:
6165:
6160:
6151:
6142:
6133:
6124:
6115:
6104:. Retrieved
6100:
6091:
6082:
6062:
6011:
6009:as a whole.
5968:
5947:
5943:
5908:
5899:
5895:
5874:
5810:
5802:
5798:
5791:
5604:
5562:
5411:
5343:
5340:
5333:
4728:
4172:
4046:
4033:
4026:
3974:
3840:
3509:
3400:
3345:
3341:
3236:
3098:
2967:
2964:
2944:
2931:
2926:
2902:
2900:
2892:
2871:
2850:preamplifier
2838:
2817:
2805:
2801:
2704:
2700:
2657:
2653:
2618:
2526:
2473:
2337:
2309:
2187:
2109:
2031:
1938:
682:
480:
262:
149:
142:
136:
130:
122:
102:
85:
61:
59:
54:
50:
48:
23:
19:
18:
5803:practically
5238:where
4756:R\ll X_{L},
4349:where
2970:capacitance
2952:phase angle
2846:moving coil
28:electronics
6222:Categories
6106:2018-09-25
6075:References
5336:Inductance
2781:See also:
1951:ripple-rms
71:and other
36:DC voltage
6035:Rectifier
6016:from the
5963:prototype
5833:π
5824:ω
5797:>>
5756:≈
5744:ω
5713:ω
5619:γ
5585:π
5576:ω
5515:≈
5497:ω
5484:⋅
5426:γ
5369:π
5302:≪
5262:≈
5228:ω
5188:ω
5164:π
5121:ω
5109:⋅
5103:π
5009:γ
4989:≪
4910:π
4850:−
4835:π
4739:≪
4688:⋅
4682:π
4597:⋅
4579:π
4501:⋅
4494:π
4477:ω
4466:ω
4460:
4430:π
4417:π
4325:⋅
4297:ω
4288:
4279:π
4226:∫
4150:ω
4141:
4132:π
4053:harmonics
3988:γ
3938:≈
3848:γ
2812:talk page
2777:Filtering
2721:≈
2683:%
2668:≈
2665:η
2509:≈
2492:π
2453:π
2320:≈
2317:γ
2287:−
2273:π
2233:−
2201:γ
2170:π
2082:
2012:−
1998:π
1988:π
1905:π
1868:−
1777:π
1730:π
1721:−
1611:let
1595:π
1551:−
1542:π
1502:π
1485:π
1446:
1397:
1357:−
1309:π
1237:−
1190:∫
1150:−
1110:∫
1075:−
1042:π
992:
986:−
983:−
977:π
971:
965:−
955:π
923:π
897:
891:−
879:π
809:∫
661:ω
652:
643:π
522:π
458:ω
446:
440:⋅
421:−
410:π
401:
390:∞
375:∑
371:⋅
366:π
329:π
232:
221:⋅
152:rectifier
81:frequency
6029:See also
6022:stopband
6018:passband
6014:roll-off
6007:passband
5993:and the
5880:Π-filter
5877:low-pass
3197:fullwave
2881:kHz to 1
1670: so
44:waveform
32:periodic
6020:to the
5920:higher)
5811:where
5563:where
3264:gives,
3099:where
2993:current
2945:If the
2182:radians
6041:Dynamo
5402:
5398:
3975:where
3794:where
3552:where
3401:where
2927:linear
2915:
2907:
2883:
2879:
2858:
2804:about
2750:
2744:
2734:bridge
2727:
2674:
2032:where
579:where
160:
156:
69:filter
65:ripple
20:Ripple
6054:Notes
5759:0.471
5518:0.471
5269:0.471
4049:choke
3941:0.453
2903:order
2895:choke
2885:MHz.
2747:0.692
2724:0.812
2671:0.812
2323:0.483
26:) in
4729:For
3014:are
2991:and
2680:81.2
2512:1.11
109:HVDC
5790:if
5346:is
5338:.)
4457:sin
4285:cos
4138:cos
3610:is
3319:ave
3309:ave
3182:ave
3152:ave
3075:ave
3065:ave
2923:ESR
2919:DCR
2079:sin
1443:cos
1394:sin
989:cos
968:cos
894:cos
649:cos
443:cos
398:cos
229:sin
53:or
6224::
6182:^
6099:.
5989:,
5409:.
4032:≪
3280:pp
3250:pp
3044:pp
2842:IC
147:.
95:.
6109:.
5857:R
5836:f
5830:2
5827:=
5799:R
5795:L
5792:R
5776:R
5770:C
5765:X
5750:R
5747:C
5739:2
5734:3
5730:1
5725:=
5719:R
5716:C
5708:2
5703:3
5698:)
5689:L
5684:R
5680:R
5675:+
5672:1
5668:(
5662:=
5654:C
5651:D
5646:V
5639:s
5636:m
5633:r
5628:V
5622:=
5588:f
5582:2
5579:=
5541:L
5536:X
5529:C
5524:X
5509:L
5506:C
5501:2
5493:4
5489:1
5479:3
5475:2
5469:=
5461:C
5458:D
5453:V
5446:s
5443:m
5440:r
5435:V
5429:=
5381:)
5378:f
5375:3
5372:(
5366:2
5362:R
5357:=
5354:L
5315:.
5310:L
5306:X
5299:R
5291:,
5283:L
5278:X
5274:R
5250:;
5242:L
5234:,
5231:L
5225:2
5222:=
5216:L
5211:X
5197:.
5191:L
5183:2
5178:3
5174:R
5169:=
5155:p
5151:C
5147:A
5142:V
5138:2
5131:/
5124:L
5118:2
5114:R
5098:2
5093:3
5083:p
5079:C
5075:A
5070:V
5066:4
5056:=
5048:C
5045:D
5040:V
5033:s
5030:m
5027:r
5022:V
5012:=
5002:.
4997:L
4993:X
4986:R
4974:2
4968:L
4963:X
4957:2
4953:R
4947:K
4944:=
4939:2
4933:s
4930:m
4927:r
4922:V
4901:p
4897:C
4893:A
4888:V
4884:2
4878:=
4871:2
4865:s
4862:m
4859:r
4854:V
4845:2
4840:)
4826:p
4822:C
4818:A
4813:V
4809:2
4803:(
4792:=
4786:C
4783:D
4778:V
4752:,
4747:L
4743:X
4736:R
4710:.
4702:L
4697:X
4693:R
4677:2
4672:3
4662:p
4658:C
4654:A
4649:V
4645:4
4639:=
4631:2
4625:L
4620:X
4616:+
4611:2
4607:R
4602:R
4591:2
4588:1
4576:3
4566:p
4562:C
4558:A
4553:V
4549:4
4543:=
4535:2
4529:L
4524:X
4520:+
4515:2
4511:R
4506:R
4489:0
4484:]
4474:4
4469:t
4463:2
4451:+
4446:2
4443:t
4437:[
4427:1
4414:3
4404:p
4400:C
4396:A
4391:V
4387:4
4377:=
4362:L
4359:R
4354:Z
4337:L
4334:R
4329:Z
4320:t
4317:d
4312:2
4307:)
4303:)
4300:t
4294:2
4291:(
4276:3
4266:p
4262:C
4258:A
4253:V
4249:4
4242:(
4235:T
4230:0
4220:T
4217:1
4206:=
4200:s
4197:m
4194:r
4189:V
4156:)
4153:t
4147:2
4144:(
4129:3
4119:p
4115:C
4111:A
4106:V
4102:4
4096:=
4093:)
4090:t
4087:(
4081:f
4078:2
4073:V
4034:R
4030:C
4027:X
4010:R
3958:R
3952:C
3947:X
3916:R
3913:C
3910:f
3905:3
3900:4
3896:1
3891:=
3883:C
3880:D
3875:V
3868:s
3865:m
3862:r
3857:V
3851:=
3823:R
3820:I
3817:=
3811:C
3808:D
3803:V
3779:R
3776:C
3773:f
3768:3
3763:4
3756:C
3753:D
3748:V
3742:=
3736:C
3733:f
3728:3
3723:4
3719:I
3714:=
3706:3
3701:2
3694:p
3691:p
3686:V
3680:=
3674:s
3671:m
3668:r
3663:V
3635:2
3629:p
3626:p
3621:V
3595:p
3590:V
3566:p
3561:V
3537:3
3530:p
3525:V
3492:C
3470:f
3448:I
3423:p
3420:p
3415:V
3383:C
3380:f
3377:2
3373:I
3368:=
3362:p
3359:p
3354:V
3325:C
3315:t
3305:I
3298:=
3293:C
3290:Q
3285:=
3276:V
3246:V
3219:f
3216:2
3212:1
3207:=
3202:2
3193:t
3187:=
3178:t
3148:t
3127:t
3107:Q
3080:,
3071:t
3061:I
3057:=
3054:Q
3040:V
3036:C
3033:=
3030:Q
3002:I
2979:C
2822:)
2818:(
2814:.
2806:T
2761:)
2753:(
2741:;
2738:)
2730:(
2718:F
2715:U
2712:T
2686:)
2677:(
2637:2
2632:=
2629:F
2626:P
2597:2
2588:p
2584:C
2580:A
2575:V
2565:p
2561:C
2557:A
2552:V
2546:=
2543:F
2540:P
2501:2
2496:2
2487:=
2484:F
2481:F
2444:p
2440:C
2436:A
2431:V
2427:2
2420:2
2411:p
2407:C
2403:A
2398:V
2391:=
2383:C
2380:D
2375:V
2368:L
2363:V
2357:=
2354:F
2351:F
2290:1
2282:8
2277:2
2265:=
2257:C
2254:D
2249:V
2242:s
2239:m
2236:r
2230:e
2227:l
2224:p
2221:p
2218:i
2215:r
2210:V
2204:=
2147:L
2142:V
2121:T
2110:T
2095:|
2091:)
2088:t
2085:(
2075:|
2051:L
2046:V
2015:1
2007:8
2002:2
1979:p
1975:C
1971:A
1966:V
1962:2
1956:=
1947:V
1915:2
1910:)
1896:p
1892:C
1888:A
1883:V
1879:2
1873:(
1863:2
1858:)
1852:2
1843:p
1839:C
1835:A
1830:V
1824:(
1817:=
1810:2
1802:p
1798:C
1794:A
1789:V
1781:2
1773:4
1768:+
1763:2
1755:p
1751:C
1747:A
1742:V
1734:2
1726:8
1716:2
1711:2
1703:p
1699:C
1695:A
1690:V
1678:=
1666:,
1658:p
1654:C
1650:A
1645:V
1636:,
1630:C
1627:D
1622:V
1618:=
1615:K
1599:)
1590:2
1586:K
1582:+
1574:p
1570:C
1566:A
1561:V
1557:K
1554:4
1546:2
1537:2
1529:p
1525:C
1521:A
1516:V
1508:(
1499:1
1492:=
1480:0
1475:]
1471:t
1466:2
1462:K
1458:+
1455:)
1452:t
1449:(
1440:K
1432:p
1428:C
1424:A
1419:V
1415:2
1412:+
1409:)
1406:t
1403:2
1400:(
1389:4
1384:2
1376:p
1372:C
1368:A
1363:V
1354:t
1349:2
1344:2
1336:p
1332:C
1328:A
1323:V
1316:[
1306:1
1295:=
1286:t
1283:d
1280:)
1275:2
1271:K
1267:+
1264:)
1261:t
1258:(
1252:L
1247:V
1243:K
1240:2
1231:2
1227:)
1223:t
1220:(
1214:L
1209:V
1205:(
1199:T
1194:0
1184:T
1181:1
1174:=
1169:t
1166:d
1161:2
1157:)
1153:K
1146:)
1143:t
1140:(
1134:L
1129:V
1125:(
1119:T
1114:0
1104:T
1101:1
1090:=
1084:s
1081:m
1078:r
1072:e
1069:l
1066:p
1063:p
1060:i
1057:r
1052:V
1033:p
1029:C
1025:A
1020:V
1016:2
1010:=
1005:)
1001:)
998:0
995:(
980:)
974:(
961:(
947:p
943:C
939:A
934:V
928:=
918:0
912:]
906:)
903:t
900:(
886:[
871:p
867:C
863:A
858:V
852:=
849:t
846:d
842:)
839:t
836:(
830:L
825:V
818:T
813:0
803:T
800:1
791:=
785:C
782:D
777:V
760:2
751:p
747:C
743:A
738:V
732:=
726:C
723:A
718:V
710:=
704:L
699:V
667:)
664:t
658:2
655:(
640:3
630:p
626:C
622:A
617:V
613:4
587:n
563:2
559:n
555:1
513:p
509:C
505:A
500:V
496:2
464:)
461:t
455:n
452:2
449:(
432:2
428:n
424:4
418:1
413:)
407:n
404:(
385:1
382:=
379:n
357:p
353:C
349:A
344:V
340:4
334:+
320:p
316:C
312:A
307:V
303:2
297:=
294:)
291:t
288:(
282:L
277:V
245:|
241:)
238:t
235:(
225:|
213:p
209:C
205:A
200:V
196:=
193:)
190:t
187:(
181:L
176:V
137:η
131:γ
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