Building a Low-Frequency (Audio) Sine Generator

    Many years ago I built this low-frequency signal generator which is quite simple and has given me good service over the years.  Recently I had to open it to repair it and decided to reverse engineer the schematic diagram which I could not find anywhere in my files.  In the process of doing that I studied the circuit in detail and built a second unit just for the purpose of experimenting with it.  The circuit is quite simple and can be built quite easily. 
    It is a very simple amplifier with three stages and feedback through an RC filter network which sets the frequency.  I have seen these called "Wien bridge" oscillators but this is not really a full bridge as it only has one of the two branches.  Let us look at the feedback network first because that is the heart of the oscillator.
    From the emitter of TR3 we have both positive and negative feedback to TR1.  Positive feedback to the base of TR1 and negative feedback to the emitter of TR1.  The positive feedback is what causes the oscillator to oscillate in the first place and the variable negative feedback is needed to stabilize the amplitude of the oscillations and prevent the amplitude from becoming too large which would cause clipping and distortion.
    The positive feedback circuit is formed by two capacitors and two resistors of the same value.  The upper resistor and capacitor, in series with the feedback, form a high-pass filter while the lower resistor and capacitor, in parallel with the feedback, form a low pass filter which shunts lower frequencies to ground.  Both parts form a voltage divider and with a little math we can see that the voltage at the center of the divider, that is the feedback voltage, has a maximum absolute value and is exactly in phase for a frequency (omega) = 1 / RC.   That is the frequency at which the circuit will oscillate.  For other frequencies there will be a phase difference and the amplitude (absolute value) of the voltage feedback will be lower.  The maximum feedback voltage at that frequency is 1/3 of the output value which means we need an amplifier with a gain A of at least 3 in order to maintain the oscillations. 
    In the graph we can see in blue the amplitude of the feedback voltage at the divider in blue and in red the phase of the feedback which starts at 90 for very low frequencies, crosses zero for the critical frequency and gradually moves to -90 for higher frequencies.
    By varying the value of both R or both C we can change the frequency of the oscillation.  It is generally easier to vary the R by using a potentiometer and that is what most LF generators do.  We want the maximum frequency in each range to be about ten times the minimum frequency so we add in series with the pot a resistor with a value of about 1/10 of the value of the pot resistance.  This gives us a resistance range from 1R to 11R which means the frequency range is also 1:11 which works well as it gives us about 5% extra over and under the strict 1:10 ratio. 
    Here is how we calculate the values of R and C.  Suppose we have a double 10K pot and we want to have an oscillation range from 1Khz to 10Khz.  first we add in series with the pot a resistor of 1K which gives us a resistor range from 1K to 11K.  When at 11K, max resistance, we will get lowest frequency which is 1Khz but we go 5% lower to 950 hz.  By using the above formula we get C = 15 nF.  Adjusting the value of R to the min of 1K we get a frequency of 10.6 Khz which is good.  This 5% range extension at each end allows for component tolerance values. 
    To obtain several ranges we maintain the same pot value and switch the capacitors so that we have:
Nominal Range Actual Range C
10 - 100 hz 9.5 - 106 hz 1.5 uF
100 - 1000 hz 95 - 1060 hz 150 nF
1 - 10 Khz 0.950 - 10.6 Khz 15 nF
10 - 100 Khz 9.5 - 106 Khz 1.5 nF
100 - 1000 Khz 95 - 1060 Khz 150 pF

    Strictly for audio applications we could do with three ranges: 20 - 200 hz, 200 hz - 2 Khz, 2 - 20 Khz. 
    It is also possible to fit a fine adjustment pot in series with the main one.  If, say, we fit in each branch a 10K coarse adjustment pot, a 1K fine adjustment pot and a 1K1 fixed resistor then the ratio between lowest and highest frequencies would still be 11 and we would have to adjust the C value accordingly.
    Choosing a potentiometer
    We have already chosen a value of 10K but this is only the beginning.  We have already said that the output frequency is inversely proportional to the value of R.  The value of a linear pot grows linearly with the position of the cursor so that if we connect it normally we will have the highest frequency at the lowest end and the lowest frequency at the highest end.  This is easy enough to solve by using the cursor and higher end of the pot so that resistance diminishes as the cursor advances.  That way the frequency grows as the cursor advances.  That is the way my old generator is wired but it still has a slight problem.  As the resistance decreases linearly, the frequency, which is proportional to the inverse of the resistance, rises exponentially.  You can see this effect on the graph on the right where the blue line represents the resistance value of the pot not counting the external fixed resistor and the red line represents the output frequency of the oscillator.  We can see that the output frequency rises very slowly at first but at the end of the range it rises very fast and it would be difficult to obtain a given frequency with precision. 
    To correct this we would need a pot where the resistance would decrease very fast at first and later decrease much more slowly.  This is called an antilog pot because it does the opposite of what a logarithmic pot does.  The resistance of a log pot rises very slowly at first and then rises very fast at the end.  The rule is that the first 50% turn increases the resistance by only 10% of the total while the remaining 50% turn increases the resistance by the remaining 90%.  An antilog pot does the oposite: the first 50% turn increases the resistance to 90%. 
    The chart on the right shows an antilog pot behavior.  The blue line represents the resistance which falls fast at first and slower later.  You can see it is not truly logarithmic but just an approximation with two linear segments.  The resulting output frequency (in red) does not rise linearly but rather with two exponential segments which come closer to a linear function but are still curved.  Still this is better than using a linear pot so, if you can find an antilog double pot then this is the way to go.
Cursor       Frequency
Position  Lin.Pot   Antilog Pot
     0      955      955 <- Coincidence at start of scale
     5     1000     1040
    10     1050     1141
    15     1105     1265
    20     1167     1419
    25     1235     1615 <- Linear would be 3573
    30     1313     1875
    35     1400     2234
    40     1500     2763
    45     1615     3621
    50     1750     5250 <- Note the difference
    55     1909     5526
    60     2100     5833
    65     2333     6176
    70     2625     6563
    75     3000     7000 <- Note the difference
    80     3500     7500
    85     4200     8077
    90     5250     8750
    95     7000     9545
   100    10500    10500 <- Coincidence at end of scale
    Because antilog pots are difficult to find most designs and kits use linear pots and the owner just lives with the frequency scale compressed into the upper part of the dial.  In linear pots the resistance *increases* linearly with cursor position but here we need it to decrease linearly.  No problem, we just reverse the way it is connected and the resistance decreases linearly and that way the frequency rises as the cursor advances.  Could we use a logarithmic pot by similarly using the upper pot connection instead of the lower one?  The answer is that it will not work.  The blue line on the chart on the right represents the resistance between the cursor and the lower end of a logarithmic pot and the red line represents the resistance between the cursor and the upper end.  None of them will work for us directly but we can work around this.
    We can use a log pot and get the more linear response we want but then the frequency will decrease with increasing cursor position as seen in the graph at right which creates an undesirable situation.  If, as is common case, the scale is fixed on the front panel and the indicator is fixed to the knob which turns the pot then the higher frequency will be at the beginning (left side) of the scale and the lowest frequency at the upper end (right hand side) of the dial.  (See illustration.)  Some people might not mind this but most people are used to clockwise increasing and counterclockwise decreasing and would prefer it that way. 
    A solution is to have the scale on a circle which turns with the pot shaft and the indicator fixed of the front panel.  The circular scale can be positioned outside the box, in front of the front panel, or it can go inside the box, behind the front panel and the indicated frequency visible through a window cut in the front panel.  This has the advantage that the circular scale is more protected. 
    Another type of solution is to use pulleys.  This allows better precision and control and allows reversing rotation direction in any way we might need. 
    Power Supply
    It is powered at 20 V and uses about 20 mA.  The supply must be stabilised or the ripple will show in the output signal.  This is the diagram of the power supply I used but you can use pretty much any 20 V stabilised power supply. 
    In every device I build I like to put in the back an auxiliary power output base in parallel with the power input because this allows to daisy chain the different instruments and avoids the need for big power strips.  This makes sense because the power consumption of most laboratory instruments is small.  Instruments with substantial consumption should obviously not be fed through other instruments where the total load on a single cord would be excessive. 
    I have a neon pilot light because that is what was common at the time.  Today I would use an LED fed from the DC.  A protective fuse is always a good idea although sometimes I get lazy and do not fit one with a proper receptacle and just fit it inside the box.  The transformer is a very small 24 Vac unit but probably anything from 18 to 24 Vac would work.  You just need to have some headroom above 20 V for the regulator to work.  The regulator is very simple and almost any NPN transistor will do because the consumption is under 20 mA.