Starting Point (Part 7)
Tone Boost - Here's another project that's ideal for musicians new to electronics.
As it is hoped this series will show, it is within the capabilities of practically anyone to gain a good basic understanding of electronics.
Each part of the series is accompanied by a simple constructional project which demonstrates the practical application of the theory that has been covered, as well as being a useful and worthwhile piece of equipment in its own right.
We have covered the charge storage ability of capacitors and the use of this property in timing and decoupling circuits in previous parts of 'Starting Point'. Capacitors have other important uses, probably the most common being for coupling an alternating or varying DC signal from one part of a circuit to another while blocking any steady DC component on this signal.
This property of a capacitor is easily explained with the aid of the simple circuit diagram shown in Figure 1. Assume that R1, R2 and RV1 are all of the same value, and that initially the wiper of RV1 is at the centre of its track. When power is connected to the circuit C1 will be charged by way of R1, the upper section of RV1, and R3. The current that flows gives an initial voltage across R3, but this soon subsides as the charge on C1 builds up to the point where the positive plate is at half the supply voltage and the negative plate is at the negative supply voltage. The charge current then ceases and the voltage across R3 is zero.
If the slider of RV1 is now moved towards R1, the voltage across C1 increases and it therefore charges up through R1, RV1 and R3 once again. This current flow through R3 produces a voltage across this component with the end that connects to C1 being positive of the terminal which connects to the negative supply rail. Of course, when the slider of RV1 reaches the top of its track the charge on C1 soon reaches two thirds of the supply voltage and the charge current ceases. The voltage across R3 therefore returns to zero again.
Moving the wiper of RV1 towards R2 results in a reduction in the voltage fed to C1, and it therefore discharges through the lower section of RV1, R2 and R3. This again produces a voltage across R3, but it is of the opposite polarity this time and the end which connects to C1 goes negative of the negative supply rail. Again, when the wiper of RV1 reaches the end of its track the charge on C1 quickly adjusts to equal the voltage fed to it so that no further charge current flows and the voltage on R3 returns to zero.
Thus it can be seen that C1 blocks a steady DC level from reaching R3, but a varying voltage is effectively allowed to pass through to R3. It is important to realise that the effect is as if C1 was allowing a signal to pass, but no current actually flows through C1. It is simply a matter of a charge being passed backwards and forwards from one plate to the other. Another important point to note is that although a varying DC signal is being generated by moving the wiper of RV1 up and down, the signal developed across R3 is an AC signal which is positive when RV1's slider is positive going, and negative when RV1's slider is negative going.
If R1, R2 and RV1 were to be replaced with an AC signal source the circuit action would be much the same with a charge passing through C1 in one direction during positive half cycles, and a charge passing in the opposite direction during negative half cycles, giving an AC signal across R3.
We now come to the question of how well, or otherwise, does a capacitor couple a signal to a load resistance. The factors governing the efficiency with which a capacitor couples a signal from one part of a circuit to another can be explained with the help of Figure 2. The square wave generator produces an output waveform of the type shown in Figure 3(a) and this is coupled to R1 via C1. When the output of the square wave generator changes from 0 volts to being fully positive, C1 charges up by way of R1. If C1 has a relatively low value in comparison to that of R1, C1 will quickly fully charge and the positive voltage across R1 rapidly decays to zero. When the output of the square wave generator switches back to zero volts C1 discharges through R1. With the value of C1 low in comparison to that of R1 it will discharge very rapidly so that the negative voltage produced across R1 quickly drops back to zero again. This gives the wave shape shown in Figure 3(b) across R1.
This obviously gives a rather inefficient coupling, but there are three ways of improving matters. One is to increase the frequency of the input signal so that it returns to zero volts before C1 has started to significantly charge up. There would then be practically no charge on C1 and the negative spikes of Figure 3(b) would be largely attenuated. The waveform across R1 would then resemble that of Figure 3(c). However high the input frequency is made, C1 will always have discharged slightly before the input signal returns from its positive value to zero and there will be some distortion of the wave shape. However, for all practical purposes this distortion of the waveform can be kept down to an insignificant level.
An alternative to increased input frequency is a higher value for C1 as it will then charge up to a lesser degree during the periods when the input signal is positive. The third method is to increase the value of R1, which has exactly the same effect of slowing up the charge rate of C1.
In effect, C1 and R1 form a potential divider, but C1 does not have a fixed resistance. Its resistance is infinite at DC (in theory), and with AC signals its resistance falls as frequency is increased. In fact C1 does not have true resistance at all, and the correct term is reactance. This is measured in ohms, like resistance, but needs to be specified at a particular frequency to be meaningful. There are actually two types of reactance, capacitive reactance and inductive reactance. Capacitive reactance decreases as frequency is increased, whereas inductive reactance increases as frequency is increased.
Sometimes a circuit has a combination of resistance, inductive reactance, and/or capacitive reactance, and the correct term to use is then impedance. Whereas resistance is simply calculated by dividing the applied voltage by the current flow, impedance and reactance are calculated by dividing the peak applied voltage by the peak current flow. This slight modification is necessitated by the fact that with reactance and impedance we are not dealing with static quantities of voltage and current, and peak current flow does not necessarily coincide with peak voltage.
The circuit of Figure 2 is actually a simple form of frequency selective filter and it is this filtering that causes the changing of the wave shape. At high frequencies C1 has a reactance which is low when compared to the resistance of R1, and the losses through C1 due to a potential divider action are insignificant. At low frequencies the reactance of C1 becomes large in comparison with the resistance of R1, and the losses through C1 are also large. The reactance of a capacitor is inversely proportional to the applied frequency, for example, a doubling of frequency halves the reactance value. In a filter of the type shown in Figure 2 there is only a very gradual and insignificant increase in the attenuation as the input frequency is reduced, except when the reactance of C1 starts to become significant in comparison to the value of R1. Even then, the attenuation rate of the filter can never exceed 6dB per octave (i.e. the signal level at the output can reduce by no more than 50% if the input frequency is halved).
It is the filtering effect of a circuit of the type shown in Figure 2 that gives the waveform distortion shown in Figure 3(a) and 3(b). A square wave consists of a signal at the fundamental frequency plus signals at certain harmonics (multiples) of this frequency. If the capacitor provides inadequate coupling at the fundamental frequency, the fundamental signal becomes relatively weak, and the lower frequency harmonics become weaker in comparison with the higher harmonics. This results in the distortion of the waveform, which only occurs if there are two or more frequency components present at the input. If a pure sinewave (which has just one frequency component) is fed to the filter, the signal at the output can only be changed in amplitude, not waveform.
Frequency selective filtering can also be provided if the positions of the resistor and capacitor are transposed, as shown in Figure 4. However, the filter now provides low losses at low frequencies where the value of R1 is low in relation to the reactance of C1. At high frequencies where the value of C1 becomes less than that of R1 there are large losses through R1. Thus this type of filter permits low frequency signals to pass with minimal losses, but seriously attenuates high frequency signals. The ultimate attenuation rate is again 6dB per octave.
For obvious reasons, a filter of the type shown in Figure 2 is called a high pass filter and one of the type shown in Figure 4 is a low pass filter.
Although these filters only give an ultimate roll off rate of 6dB per octave, as with any filter, a higher attenuation rate can be achieved by using two or more filters in series.
The equation for calculating capacitive reactance is:
Xc = 1000000 / 2π fC
where Xc is the capacitive reactance in ohms, C is the capacitance value in microfarads, and f is the frequency in Hertz. For example a 100nF (0.1uF) capacitor would have a reactance of approximately 159k at 100 Hz, 15.9k at 1kHz, 1.59k at 10kHz, and only 159 ohms at 100kHz.
Our constructional project this month is a bass and treble booster for use with an electric guitar. This demonstrates the use of capacitors to provide AC coupling with DC blocking, and tailoring of the frequency response. Figure 5 shows the circuit diagram of the Toneboost.
TR1 is used as an emitter follower buffer stage at the input of the unit. This merely ensures that the guitar is fed into a reasonably high impedance so that the pick-up is not so heavily loaded that the output signal level is significantly reduced. R1 and R2 bias the base of TR1 to half the supply voltage, and the emitter of TR1 will be about 0.6 volts lower than this. C1 couples the audio frequency AC signals from the pick-up into the base of TR1, but prevents the fairly low resistance of the pick-up from affecting the biasing of TR1. A capacitor used in this way is usually termed a coupling capacitor or a DC blocking capacitor. The reason for biasing the base of TR1 is to enable the output signal at its emitter to swing up and down in voltage in sympathy with the input voltage. Without this biasing the input signal could take the emitter of TR1 positive of its quiescent level, which would be zero volts. Due to the voltage drop from the base to the emitter of TR1 it would need to reach an amplitude of about 0.6 volts therefore negative input half cycles would have no effect on TR1. Biasing is therefore essential in an audio frequency amplifier.
C2 couples the signal at the emitter of TR1 to the input of the next stage, and this is a common emitter amplifier which utilises TR2. We will not consider the operation of a common emitter amplifier in detail here, but it is necessary to know that the voltage gain provided by this stage is approximately equal to the impedance in the collector circuit divided by the impedance in the emitter circuit. It is at this stage that the bass and treble boost are produced.
With S1 closed and S2 open there is roughly unity voltage gain through the circuit. There is obviously 560 ohms in the emitter circuit of TR2, but things are a little less straight forward in the collector circuit. The impedance of R6 is shunted by the parallel impedance of R8. This is coupled across R6 by the parallel capacitance of C3 and C5. These have a very low impedance at all audio frequencies so that the effect is very much the same as if R8 was directly connected across R6. This gives similar emitter and collector circuit impedance values, and the voltage gain of roughly unity through the unit.
The treble boost is switched in by closing S2 so that R7 is shunted by the impedance of R9 and C4. At low and middle audio frequencies C4 has a high reactance (about 6.5k at 50Hz for example) and does not have a large effect on the voltage gain of the circuit. At about 700Hz the impedance through R9 and C4 is comparable to that of R7, and their shunting effect on R7 gives a doubling of the circuits voltage gain. At higher frequencies the impedance of R9 and C4 steadily decreases, and the voltage gain of the circuit rises. The voltage gain is approximately 6 at 5kHz, and reaches approximately 10 at frequencies above 10kHz. The response does not continue to rise significantly above 10kHz due to the inclusion of R9 which limits the shunting effect C4 can have on R7. Although one might expect the value given to R9 to give a higher maximum gain than 10, this is not the case since TR2 has a small innate emitter resistance which is effectively connected in series with the discrete emitter impedance. The circuit therefore gives the required boost of up to about 10 at treble frequencies.
S1 is opened in order to give the bass boost, and this effectively takes C5 out of the circuit. Due to its high value R10 does not have any significant effect on the gain of the circuit, and we can ignore this component for the time being. At high and middle audio frequencies C3 has a low reactance which keeps R8 effectively shunted across R6 and the voltage gain of the circuit at about unity. At approximately 250Hz the reactance of C3 is high enough to reduce the shunting effect of R8 sufficiently to boost the voltage gain to about 2. At lower frequencies the reactance of C3 steadily increases as does the voltage gain of the circuit. The voltage gain reaches about 10 at 30Hz. Thus the required bass boost is produced. As the bass and treble boost circuits operate over different frequency ranges there is little interaction between them, and it is possible to use both at once if desired.
C6 couples the output from TR2 to the guitar amplifier, and it ensures that the amplifier does not affect the DC conditions in the booster circuit if the amplifier should have a DC path across its input. Of course, all three coupling capacitors in the circuit have values which give them a low reactance even at low audio frequencies when compared to the impedance into which there are feeding a signal. This prevents them from significantly reducing the low frequency response of the unit.
The purpose of R10 is to keep C5 charged when S1 is open. If this is not done it is likely that a large pulse would be generated at the output when S1 was closed and C5 rapidly charged up, and this could produce a very loud 'click' from the loudspeaker. The high value of R10 ensures that it does not significantly effect the circuit in other respects.
The unit is housed in a diecast aluminium box. A case of this type is ideal for a project such as this which needs a tough case that will also screen the circuitry. The case needs to be strong because S1 and S2 are both foot operated switches, and some cases would be damaged after repeated operations of these.
The general layout of the unit can be seen by referring to the photographs, but the precise layout is not critical and it is acceptable to use any layout that enables all the components to fit into the case and has the controls conveniently placed.
The small components are fitted onto a small 0.1in. matrix Veroboard panel which measures 11 copper strips by 22 holes. This board is constructed using the normal techniques, and Veropins are used at points where off-board connections are to be made. The board can then be bolted in place inside the case before it is wired to the switches, sockets, and battery connector. Use spacers over the mounting bolts so that the connections and copper strips on the underside of the board are kept away from the metal case and are not short circuited through it.
In use the guitar connects to JK1, and a screened lead fitted with a standard jack plug at each end is used to connect the booster to the amplifier. Due to the increase in gain provided by the unit at some frequencies it is necessary to take greater care to avoid significant pick-up of mains hum and stray feedback from the loudspeaker to the guitar pick-up.
Feature by Robert Penfold
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