Filtering Capacitor Capacity
To obtain the DC voltages necessary for the operation of vintage radios
(voltages applied to the grids and anodes), the
voltage from the mains (220V/50Hz in France today, but this
was not
always the case), is passed through a transformer to obtain the
necessary levels. Then the AC voltages are 'rectified'. They
are no longer alternating, but are still not continuous. By
placing a capacitor at the output of the rectifier, the DC mode is approached.
As nothing is perfect, the voltage obtained can be seen as the superposition
of a perfectly continuous voltage and residual alternating voltages
harmonics (i.e., multiples of the mains frequency). The
filtering capacitor placed after
the rectifier reduces the ripple voltage applied to the following circuits.
The higher its capacity, the less troublesome the ripple voltage will be.
In the case of a tube rectifier, this capacity will be limited to
Cmax prescribed by the diode manufacturer, under
penalty of shortening its lifespan.
There are two rectification modes: half-wave and full-wave. The first mode produces a ripple voltage whose fundamental frequency is 50Hz (60Hz in the USA). This doubles in full-wave mode.
There is a simplified relation for calculating this capacity with C(Farads), IMAX (A), URIPPLE (V) and f=50 Hz :
There are two rectification modes: half-wave and full-wave. The first mode produces a ripple voltage whose fundamental frequency is 50Hz (60Hz in the USA). This doubles in full-wave mode.
There is a simplified relation for calculating this capacity with C(Farads), IMAX (A), URIPPLE (V) and f=50 Hz :
Half-wave
$$ C=\frac{{I_{max}}}{f.u_{cc}}$$
$$ C=\frac{{I_{max}}}{f.u_{cc}}$$
Full-wave
$$ C=\frac{{I_{max}}}{2f.u_{cc}}$$
$$ C=\frac{{I_{max}}}{2f.u_{cc}}$$
Full-wave
$$ C=\frac{{I_{max}}}{4\sqrt{3}\ f\ u_{rms}}$$
$$ C=\frac{{I_{max}}}{4\sqrt{3}\ f\ u_{rms}}$$
The absolute value of the ripple voltage \(u_{cc}\) or the RMS voltage \(u_{rms}\) is not an interesting quantity for the designer. It must be related to the DC component \(u_{dc}\). This is why the ratio \(r=u_{cc}/u_{dc}\) is generally fixed, which can vary between 1 and 10%, and then C is calculated as a function of the maximum current \(I_{max}\) that will be absorbed by the downstream load circuit.
Two examples
In low voltage with full-wave rectification by silicon diode.
We want to be able to supply 120 mA at 15V with a ripple rate of 1%. We have a transformer supplying 12V RMS on the secondary. The peak voltage will be 12 x 1.414, i.e., 17V. The diodes cause a drop of about 2V. This leaves 15V peak.
The ripple voltage will be 15 V x 1% = 0.15V. The calculation gives $$C=\frac{0.12}{100 . 0.15 } = 8 000\mu F$$
We want to be able to supply 120 mA at 15V with a ripple rate of 1%. We have a transformer supplying 12V RMS on the secondary. The peak voltage will be 12 x 1.414, i.e., 17V. The diodes cause a drop of about 2V. This leaves 15V peak.
The ripple voltage will be 15 V x 1% = 0.15V. The calculation gives $$C=\frac{0.12}{100 . 0.15 } = 8 000\mu F$$
A capacity of 10 000µF/35V can be used
In high voltage, with full-wave rectification using an EZ80 tube.
The HT secondaries of a loaded transformer deliver 250V RMS, i.e., 353V peak. We must be able to supply 100 mA. The EZ80 tube supports a maximum of 50µF. Let's calculate the lowest possible ripple under these conditions. $$\begin{cases} U_{ondulation}=\frac{0.1}{100 . 50 . 10^{-6} } = 20V \\ \mbox{That is 6% ripple rate} \end{cases}$$
The HT secondaries of a loaded transformer deliver 250V RMS, i.e., 353V peak. We must be able to supply 100 mA. The EZ80 tube supports a maximum of 50µF. Let's calculate the lowest possible ripple under these conditions. $$\begin{cases} U_{ondulation}=\frac{0.1}{100 . 50 . 10^{-6} } = 20V \\ \mbox{That is 6% ripple rate} \end{cases}$$
This average result requires following
this first capacitor with a
R/C or L/C circuit to improve filtering. In vintage radios, the
last AF amplification tube (power) is less sensitive to residual
rectification voltages than the other stages. This is why it
is often powered via the first capacitor (called the head capacitor).
Filtering Capacitor Capacity Calculation Tool
