Section B7: Filtering
As mentioned at the end of the previous section, simple rectification results
in a pulsating dc voltage at the output, also known as output ripple.
These deviations from the desired dc may be reduced by the process of
filtering.
The simplest form of filter uses a single parallel resistor-capacitor
combination. Recall, from the olden days of circuit analysis, that this creates
an exponential decay curve as the capacitor discharges with a time constant
τ=RC. So (using the full-wave rectified output as an example)... what we
Therefore, the voltage ripple,
vr = ∆V = Vmax − Vmin
is significantly reduced by this technique.
NOTE: The figures above represent a rectified signal that is only positive and
is used to generate a positive dc voltage. A negative dc voltage may also be
generated by creating a purely negative signal (flipped about the time axis).
Vmax and Vmin indicate the magnitudes of the respective voltages and may be
either positive or negative.
Since we already have a resistor (the load) in all the rectifying circuits we
talked about, the challenge in designing this type of filter is to define an
appropriate (and realistic) capacitor to give us an acceptable ripple. This
ripple is defined, either explicitly or implicitly, in terms of the parameters
Vmax and Vmin. Your text presents a thorough derivation of the development
of capacitor criteria in terms of the exponential decay relationship and
available discharge time, with the result of a conservative rule of thumb for
filter design
C =
Vmax
∆VfpRL
(Equation 3.52)
where:
Vmax is the maximum voltage magnitude of the rectified signal
(positive or negative)
∆V is the ripple (Vmax-Vmin)
RL is the load resistor
fp is the output fundamental frequency.
It’s worthwhile to take a minute on this last term. The output fundamental
frequency is simply the number of pulses per second of the rectified output.
For half-wave rectification, this is simply the frequency of the input signal
(where we’ve just chopped off half of the waveform), but for full-wave
rectification this term is double the original frequency (flipped part of the
original sinusoid so that everything’s on the same side). Specifically, for a
60-Hz input:
fp=60 Hz for half-wave rectification
fp=120 Hz for full-wave rectification
A note of caution (from one who has been caught many times) -- be
careful what numbers you slap in an equation! Equation 3.52
provides a solid estimate of the capacitance required for a given
circumstance, but a factor of 2 makes a difference!
Just a couple more relationships that you may want to make note of:
¾ The rms (root-mean-square) ripple voltage, Vr(rms) is derived by
approximating the average of the ripple as ∆V/2 and the shape of the
filtered waveform as a sawtooth, or
Vr (rms) =
Vmax − Vmin
2 3
(Equation 3.54)
¾ The ripple factor is defined as the ratio of the rms ripple voltage to the
dc voltage desired. Ideally, this term would be zero (i.e., no ripple), but
practically, this may be another design constraint to satisfy.
ripple factor =
Vr (rms)
Vdc
(Equation 3.55)