Selecting A Capacitor Value For A Band-Pass Frequency
The basic rule of thumb is (I was once told, and it seems to bear out) that where
you have a series capacitor carrying the signal, and it is followed by a resistance
(or load) to ground, the reactance of the capacitor should be one seventh
the value of the resistance at the lowest frequency that you want passed.
This is a differentiator type of RC network that works as a high-pass filter,
rejecting frequencies below the band-pass threshold. (The differences in signal
amplitude either side of the threshold are not of course immediate, but follow a
slope.)
The application includes things like capacitance-fed grid resistors (most obviously).
As a guide, 1µF into 50kΩ is good for 25 Hz, so is 100nF into 500kΩ (divide
the capacitor by 10 and multiply the resistance by 10), as is 50nF into 1MΩ (divide
by 20, multiply by 20). Or, for 50 Hz, 50nF into 500kΩ, for 100 Hz, 25nF into
500kΩ – you get the general idea.
This can equally be applied to cathode (or even transistor emitter) bypass caps
– for a resistor in the range 1 – 2.2kΩ the capacitor should
be 50µF (47µF). If capacitor values are too large then you might start
having problems with low-frequency instability, and over-stressing your loudspeaker
voice coils in the extreme LF band which the speaker is not able to convert into
actual sound output, so all the energy just heats up the voice coil.
You can get the equivalent capacitance value for a specific reactance against frequency
from a reactance chart, or by the following equation:
µF = 1/(ω x F / (r/1,000,000))
where 'r' = the desired reactance in Ohms, F is the frequency and 'ω' (omega)
= 2 x π (π =
'pi', 22/7).