  24 February 2009
Author: Giorgos Lazaridis
BJT Transistor theory

Choosing the right capacitor size

In order for a coupling or bypassing capacitor to operate effectively, it must have the right size. As said before, the capacitor acts like a resistor in AC current. The resistance of a capacitor is called "impedance". Unlike resistors, capacitors do not have a fixed impedance. Instead, the impedance is determined by the frequency of the AC signal. The equation to calculate the impedance is the following:

XC = 1 / (2*Ã*F*C)

C is the capacitance in Farads, and F is the AC signal frequency in Hertz. So, a 10uF capacitor connected in series with a 1 KHz signal generator, will present an impedance of:

XC = 1 / (2 x 3.14 x 1 x 103 x 10 x 10-6) = 15.9 Ohms

So, what is the proper value for a coupling or a bypassing capacitor? There are two factors that must be taken into account: The frequency and the circuits total resistance. Let's talk about the frequency first. If the amplifier operates as a signal amplifier of a fixed circuit, then the answer is straight-forward: The frequency is the signal's frequency. But if the amplifier operates in a wide frequency range, then we must choose the worst case scenario.

Let's see an example of an audio amplifier. Audio amplifiers typically operate from 20Hz up to 20Kz. To choose the right frequency for our calculation, we must first think what we want the bypassing or coupling capacitor to do: We want this capacitor to act as a short-circuit in AC currents. In other words, we want the capacitor to present the lowest impedance possible in AC current. Since the impedance XC is reverse-proportional to the frequency F, the lowest impedance is presented at the highest frequency. Thus, the worst case scenario (highest impedance) is presented at the lowest frequency. So, in our calculations we will use the lowest frequency that the capacitor will operate at. In an audio amplifier for example, the lowest frequency is 20Hz.

The second factor is the total resistance of the circuit. Let's talk first for a coupling capacitor. In this case, we are talking about the total resistance of the circuit in series with the capacitor. Here is a simplified example of a circuit with a coupling capacitor: In this circuit, the total resistance is the sum of the internal resistance of the generator Rg, plus the internal resistance of the transistor ri.

In a circuit with a bypassing capacitor, the total resistance is the total resistance of the circuit parallel to the bypassing capacitor. Here is a simplified example of a circuit with a bypassing capacitor. In this circuit, the total resistance is the RE.

So, now we know how to choose the worst case scenario in terms of frequency, and how to calculate the total circuit resistance according to the capacitor type (coupling or bypassing). The optimum capacitor value that we choose must be 10 times smaller than the total circuit resistance, calculated for the worst case scenario.

To calculate the capacitor, we solve the impedance equation for C:

C = 1 / (2 * Ã * F * XC)

Let's see an example. In the simplified example of a circuit with a coupling capacitor shown above, Rg is 50 Ohms. ri is 2.2 KOhms and the frequency is 20Hz to 20KHz. To calculate the optimum capacitor value, we must first calculate the total resistance of the circuit in series with the capacitor:

Rtotal = 50 + 2200 = 2250 Ohms

The worst case scenario is 20Hz (lowest frequency), so the capacitor must present a resistance of less than 225,0 Ohms (Rtotal/10) at 20Hz frequency:

C = 1 / (2 * 3.14 * 20 * 225) = 35.3uF

So, the capacitor must have at least 35uF capacitance. This makes sure that the capacitor will have less than 1% effect on the total resistance of the circuit. And since the calculated value does not exist as a standard capacitor value, we choose the next bigger value - in our case that is 47uF.

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