### 6.1 Smoothing Capacitors.

Most electronic equipment (hi-fi's, radios, TV's, etc) require powering by one or more DC voltages. The ‘mains’ power supplied by the electricity companies isn't d.c., in the U.K. it arrives in the form of a 50Hz 230 Volts (rms) sinewave. This mains power has to be converted into the d.c. required. As a result, nearly all ‘mains powered’ equipment has to include a *power supply* unit which converts the mains a.c. into the required d.c. levels. Figure 6.1 illustrates a simple circuit for doing this. To understand it, we can break up its function into three parts, the *reservoir* (or *smoothing*) capacitor, the *diode*, and the *transformer*.

Since we already know something about capacitor's we'll start with that. To understand what the reservoir capacitor is doing, consider the *RC* circuit shown in figure 6.2a. This is similar to the circuit we looked at in the last part, but it's the ‘other way around’. Now, the input comes through the resistor, and the output is taken from the top of the capacitor.

If we use the same methods as part 5 we discover that this new circuit is a sort of ‘inverse’ of the high pass filter. Its voltage gain & phase effect for sinewaves are illustrated in figure 6.2. These show that:
- The circuit passes
__low__ frequencies without altering them very much and rejects __high __frequencies.
- The phase of the output signal
__lags__ behind that of the input.

Using calculus or similar methods it's possible to prove that, for circuit 6.2a, the sinewave voltage gain and phase change are given by the expressions

where is the circuit's *time constant.*

[Note we've used the magnitude (modulus) voltages in equation 1 instead of the peak-to-peak or rms voltages used in previous sections. This is OK because these values are all proportional to one another. Provided we use the same sorts of voltages for both input __and__ output, the value of the ratio will be the same.]

This circuit is called a *low pass filter* or *smoothing filter*. We can use it wherever we want to pass through low frequencies (or d.c.) and suppress any swift voltage changes. The circuit behaves in this way because the output voltage is taken from the capacitor. Hence the output voltage can only be changed by moving charge in or out of the capacitor. Any change in the input voltage can provide current, but it's level is controlled by having to squeeze through the resistor. The bigger the resistor's value, the smaller the current. The bigger the capacitor, the more charge it takes to alter it's voltage.

In the power supply circuit the capacitor acts as a charge storage *reservoir*. For reasons which will become clearer later, the diode & transformer supply regular pulses of charge which ‘top up’ the capacitor to a specific voltage. In between these pulses the capacitor provides the steady currents being drawn out of the power supply by the hi-fi amplifiers, or other circuits connected to it. Provided the capacitor's value is nice and large this means the circuits drawing current don't notice that the power from the mains is arriving in cyclic bursts & being stored in the capacitor until needed.