A capacitor input filter (in which the first component is a shunt capacitor) and choke input filter (which has a series
choke 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 (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). The number of reactive components in a filter is called its
order. Each reactive component reduces signal strength by 6dB/octave above (or below for a high-pass filter) the
corner frequency of the filter, so that a 2nd-order low-pass filter for example, reduces signal strength by 12dB/octave above the corner frequency. Resistive components (including resistors and parasitic elements like the
DCR of chokes and
ESR of capacitors) also reduce signal strength, but their effect is
linear, and does not vary with frequency. A common arrangement is to allow the rectifier to work into a large
smoothing capacitor 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 to the reservoir until peak voltage is again reached.
As a function of load resistance If the
RC time constant 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
phase angle 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. With the above assumptions the peak-to-peak ripple voltage can be calculated as: The definition of
capacitance C and
current I are : \begin{align} & Q = CV_\text{pp} \\ & Q=I_\text{ave}t_\text{ave}, \end{align} where Q is the amount of charge. The current and time t 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 t_\text{ave} would then be equal to half the period of the full wave input. :t_\text{ave}=\frac{t_\text{fullwave}}{2}=\frac{1}{2f} Combining the three equations above to determine V_\text{pp} gives, :V_\text{pp}=\frac{Q}{C}=\frac{I_\text{ave}t_\text{ave}}{C} Thus, for a full-wave rectifier: {{equation box 1|indent=::|equation=V_\mathrm{pp} = \frac{I}{2fC}}} where :*V_\mathrm{pp} is the peak-to-peak ripple voltage :*I is the current in the circuit :*f is the source (line) frequency of the AC power :*C is the capacitance 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
sawtooth waveform is a similar assumption to the ones above. The RMS value of a sawtooth wave is \frac {V_\mathrm{p}}{\sqrt 3} where V_\mathrm{p} is peak voltage. With the further approximation that V_\mathrm{p} is \frac {V_\mathrm{pp}}{2}, it yields the result: ::V_\mathrm{rms} = \frac{V_\mathrm{pp}}{2 \sqrt 3} = \frac{I}{4 \sqrt 3 fC} = \frac{V_\mathrm{DC}}{4 \sqrt 3 fCR} where V_\mathrm{DC} = IR {{equation box 1|indent=::|equation=\gamma = \frac {V_\mathrm{rms}}{V_\mathrm{DC}} = \frac{1}{4\sqrt 3 fCR} \approx 0.453 \frac {X_\mathrm{C}}{R}}} where :*\gamma is the ripple factor :*R is the resistance of the load :*For the approximated formula, it is assumed that
XC ≪
R; this is a little larger than the actual value because a sawtooth wave comprises odd harmonics that aren't present in the rectified voltage.
As a function of series choke Another approach to reducing ripple is to use a series
choke. A choke has a filtering action and consequently produces a smoother waveform with fewer high-order
harmonics. Against this, the DC output is close to the average input voltage as opposed to the voltage with the
reservoir capacitor which is close to the peak input voltage. Starting with the Fourier term for the second harmonic, and ignoring higher-order harmonics, ::V_\mathrm{2f}(t) = \frac {4 V_\mathrm{AC_p}}{3 \pi}\cos(2 \omega t) the ripple factor is given by: : \begin{align} V_\mathrm{rms} = {} & \sqrt {\frac {1}{T}\int_0^T \left ( \frac {4 V_\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} \\[8pt] = {} & \frac {4 V_\mathrm{AC_p}}{3 \pi}\sqrt { \frac {1}{\pi}\left [ \frac {t}{2} + \frac {\sin 2\omega t}{4\omega}\right]_0^\pi} \cdot \frac {R}{\sqrt {R^2 + X_\mathrm{L}^2} } = \frac {4 V_\mathrm{AC_p}}{3 \pi} \sqrt {\frac {1}{2}} \cdot \frac {R}{\sqrt {R^2 + X_\mathrm{L}^2} } = \frac {4 V_\mathrm{AC_p}}{3 \sqrt 2 \pi} \cdot \frac {R}{X_\mathrm{L}}. \end{align} For R \ll X_L, : \begin{align} V_\mathrm{DC} = {} & \sqrt {\left (\frac{2 V_\mathrm{AC_p}}{\pi}\right )^2 - V_\mathrm{rms}^2} = \frac{2 V_\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. \\[8pt] \gamma = {} & \frac {V_\mathrm{rms}}{V_\mathrm{DC}} = \left. \frac {4 V_\mathrm{AC_p}}{3 \sqrt 2 \pi} \cdot \frac {R}{2 \omega L} \right/ \frac{2 V_\mathrm{AC_p}}{\pi} = \frac{R}{3 \sqrt 2 \omega L}. \\[8pt] & \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{align} This is a little less than 0.483 because higher-order harmonics were omitted from consideration. (See
Inductance.) 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 input voltage; in effect, the inductor will behave like a capacitor. That minimum inductance, called the
critical inductance is L = \frac {R}{2 \pi (3f)} where R is the load resistance and f the line frequency. This gives values of L = R/1131 (often stated as R/1130) for 60Hz mains rectification, and L = R/942 for 50Hz 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
flyback voltage. 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 independent of load current. The ripple factor is: ::\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}} where :*\omega = 2 \pi f 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 ::\gamma = \frac {V_\mathrm{rms}}{V_\mathrm{DC}} = \frac {\left( 1 + \frac {R}{R_\mathrm L} \right)}{3 \sqrt 2 \omega C R} = \frac {1}{3 \sqrt 2 \omega C R}\approx 0.471 \frac{X_\mathrm{C}}{R} if
RL >>
R, which makes an RC filter section
practically independent of load where :*\omega = 2 \pi f :*R is the resistance of the filter resistor 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
low-pass Π-filter. 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.
Voltage regulation 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 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. 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 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.
Effects of ripple Ripple is undesirable in many electronic applications for a variety of reasons: • ripple represents wasted power that cannot be utilized by a circuit that requires direct current • ripple will cause heating in DC circuit components due to current passing through parasitic elements like ESR of capacitors • 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 higher) • transformers that supply ripple current to capacitive input circuits will need to have VA ratings that exceed their load (watt) ratings • 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. • 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. • 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. • 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. ==Ripple current==