##### Hi-Fi

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## Hi-Fi | |

## Tone Controls |

In response to a recent letter I thought I would concentrate on tone controls this month. Basically there are two opposing views on this subject. There are those who deny totally the need for controls. Others argue, just as vociferously, that even with the perfect system the listening room will adversely affect the sound.

To understand the operation of tone controls we need to go back to basic electronic theory. Figure 1a shows a low pass filter and Figure 1b a high pass filter. Both these filters rely on the behaviour of capacitors when fed with AC voltages. Capacitors exhibit an impedance to an AC signal which, like resistance, is measured in ohms. Unlike resistors though capacitive impedance alters with frequency. As the frequency increases the impedance decreases. Knowing this information we can understand qualitatively the action of the circuits shown in Figure 1.

Look at the low pass section. The input signal is applied through the resistor which forms a potential divider with the capacitor. The output signal is taken from across the capacitor. At low frequencies the impedance of the capacitor is much higher than the resistor's value. Because of this the output signal at these frequencies is hardly attenuated by the capacitor's impedance. At high frequencies the capacitor looks like a low impedance. In consequence the output signal is highly attenuated.

The high pass filter section works in the reverse manner because the components have been transposed.

Now it is possible to obtain relative boosts and cut in both the bass and treble regions with modifications of the simple passive circuits shown. The big breakthrough as far as hi-fi is concerned came when these simple circuits were replaced with active circuitry. Before passing on to this let's look again briefly at the simple filters.

The impedance of the capacitor can be found from the following equation, Z = 1/2ΠfC, where Z is the impedance in ohms, f is the input frequency in Hertz and C the capacitance in Farads.

The cutoff point of the filters shown, the legendary 3dB point, occurs where the impedance of the capacitor is equal to the resistance to which it is connected. To take an example let's assume that the resistor is 100k and the capacitor is 100nF. The 3dB point will occur when the impedance of the capacitor is equal to the value of the resistor, 100k. By rearranging the equation for f we get, f = 1/2ΠCZ = 1/(6.28 x 10^{-7} x 10^{5}) = 15.9Hz. The high pass filter will have a response flat above that frequency, that falls at 6dB/octave below it. The low pass filter will have the converse response.

At this point Peter Baxandall enters the picture. The tone control circuit that bears his name and is found in virtually all preamplifiers has been around for a long time now (it first saw the light of day in the fifties!).

To understand how it works once again requires an excursion into basic circuitry, this time amplifiers. Look now at Figure 2a. This shows an op-amp circuit, the so-called virtual earth circuit. To understand its operation it is important to know what the op-amp is doing. The non-inverting input is held at earth potential. The op-amp operates to ensure that both its inputs stay at the same potential. If a positive voltage is fed into R1 with respect to earth a current will flow through the resistor equal to Vin/R1. In order that the inverting input stays at earth potential it is necessary that this current flows somewhere. The 'somewhere' is to the output stage via R2. The output voltage will therefore go negative to sink the input current.

Because the same current flows through both - resistors the gain of the circuit is R2/R1.

If either resistor were to be replaced with a capacitor the same relationship holds true, but the gain will vary with frequency. Figure 2b shows how this information is used to construct a bass boost and cut circuit. With the slider of RV1 in the midway position the gain of the circuit will be unity since the network is symmetrical. Now let us assume that the slider, and hence the inverting input is at the right hand end of its travel, C2 will be shorted out and the whole of RV1 will appear in the input circuit.

At high frequencies C1's impedance will be negligible compared with either RV1 or Rl. The gain of the circuit will be determined by the ratio of R2/(RV1+R1) unity. As the input frequency is lowered a point will be reached where the impedance of C1 is equal to R1. Here the response will be 3dB down. The response will continue to fall until the impedance of C1 equals the resistance of RV1. At this stage the response is 3dB up referred to the minimum gain of the circuit which occurs at DC.

What we have just described is a bass cut control. The beauty of this circuit is that with the slider at the opposite end of the pot, bass boost is obtained. Imagine the situation, C1 is effectively shorted and RV1 is between the output and inverting input. At very low frequencies the gain is RV1 + R/R. As the frequency increases C2 will begin to shunt RV1. The response starts to fall when C_{Z} equals RV1 then falls to the +3dB point where C_{Z} = R.

Figure 2c shows the treble boost and cut control. With the slider in the central position the gain of the circuit is again unity at any frequency. With the slider to the right maximum cut is obtained since at high frequencies the impedance of C is negligible. The gain being R2/(RV1+R1). With the slider to the left maximum gain occurs at high frequencies.

The full circuit of a Baxandall tone control is shown in Figure 3. As you can see this consists of both of the sections discussed. Note though that R5 and R6 have been included to prevent interaction between them. The circuit shows only one channel. For stereo duplicate everything but use dual gang pots for RV1 and 2 to ensure tracking.

*Feature
by Jeff Macaulay*

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