Coupling Capacitors: Value & Uses

[Pagedown]

When you need to couple ac signals you use coupling capacitors. How do we decide its value and what are the uses of coupling capacitors?

 

[Averagesupernova]

This sounds like homework.

 

[Studiot]

The coupling capacitor forms an L shaped potential divider with the input impedance of the following stage.

So the signal is divided in the normal manner across the impedance of the coupling cap and the input impedance (in series).

Since you want the signal to be largely across the imput impedance you make the coupling cap such that its impedance is small compared with the input impedance at signal frequencies: 1/10 is good.

go well

 

[Pagedown]

you mean like a voltage divider? why would we need to use a voltage divider when we want to couple the whole voltage across?

 

[Averagesupernova]

I thought Studiots explanation was confusing although it is correct. Ideally you would lose no voltage across the coupling capacitor but in the real world you will lose some. Pick a capacitor that couples as much signal as you can but not of such a large capacitance that it takes the circuit a long time to establish its DC operating point after power is first applied due to charging of the capacitor.

 

[Studiot]

No I don't mean like a voltage divider. I mean the circuit arrangement is a voltage divider.

Perhaps the attached sketch will help.
Since you have no particular circuit in mind I've kept it general.

The first sketch shows two single ended stages or amplifiers A1 & A2, the first feeding the second via coupling capacitor C1 the second feeding a load via coupling capacitor C2.

It is worth noting that we use (need) coupling capacitors because the DC levels at the stages may not be (probably are not) the same so we block DC whilst allowing the AC signal through.

The second sketch shows how the signal from a stage is applied.

The stage output impedance is inseries with the coupling capacitor and the input impedance of the next stage.

It is normal to make Z_load>> Z_out and in general we choose circuit values so this is the case and we then ignore Z_out.

We want the bulk of the signal to appear across Z_in or Z_load, not across Z_capacitor so we choose the capacitor so that

Z_load>> Z_capacitor

To put some real values into the example, say the first stage is a preamp with an output impedance of 600 Ohms and the second stage is a power amp with an input impedance of 10K.

We seek a capacitor impedance that will be less than 1/10 the input impedance of the power amp ie 1k.
Say our lowest frequency of interest is 100 Hz then

$${C_1} = \frac{1}{{2\pi f{X_c}}} = \frac{1}{{2\pi {{10}^2}{{10}^3}}} = \frac{{10*{{10}^{ - 6}}}}{{2\pi }}microfarads \approx 1.5\mu F$$

For the power amp feeding an 10 ohm loudspeaker the output impedance is usually less than 0.1 ohm and again may be neglected.

A 100 Hz calculation for C₂ shows

$${C_2} = \frac{1}{{2\pi f{X_c}}} = \frac{1}{{2\pi {{10}^2}1}} = \frac{{{{10}^4}*{{10}^{ - 6}}}}{{2\pi }}microfarads \approx 1500\mu F$$

So you can see why we have large speaker coupling capacitors and small inter amplifier caps.

go well