Written by Bryce Ringwood

As mentioned in the article on the Superhet, the signal frequency (station frequency you are trying to receive) mixes with the local oscillator frequency to produce an intermediate frequency. For  example, suppose you want to receive Hellenic Radio on 1.422MHz, and you have designed your radio to have an intermediate frequency amplifier operating on .455MHz, then you would need a local oscillator operating at 1.422 + .455 = 1.877MHz.

This is easy enough if we only were to have a single frequency to consider. In a supehet receiver covering .55MHz to 1.6MHz, the local oscillator must (as far as possible) keep in step with or "track" the received frequency. From the formulae for resonant circuits, it will be apparent that if a two (or more) gang tuning capacitor is used, then the capacitance variation must be less for the local oscillator tuned circuit than for the signal frequency circuit. To reduce the swing, we use a padder  capacitor $C_p$, as illustrated in the following diagram:

Superhet Signal and Osillator Tuned Circuits

I have not shown all the other bits and bobs of the mixer circuit. Note that the two trimmer capacitor values include stray capacitance from the wiring, valve electrodes (or transistor internal capacitances) - so you will have to remember to subtract these from whatever the program calculates.

The calculation is rather horrible, so we have to have a strategy. First we calculate the values of $L_1$ and $C_{t1}$, knowing the minimum and maximum possible value of $C$. Next we choose a frequency somewhere near the middle of the dial - commonly $\sqrt({f_1}{f_3})$ where $f_1$ and $f_3$ are the minimum and maximum frequencies we wish to tune in to. This will provide us with values for the inductance $L_1$ and the trimmer. By the way - you will have to measure the maximum and minimum values for $C$.

The next step is to calculate the  unknown values for the padder $C_p$, the trimmer $C_{t2}$ and the oscillator inductance $L_2$, knowing $f_1$,$f_2$ and $f_3$.

Finally,you need to look at the results to assess whether what you are trying to do is really practical (That junk-box 3 gang 75pf variable capacitor probably can't tune the entire medium wave band.) You do need to choose a padder as close as possible to the calculated value and deduct 8pf or so from the trimmer values.  You can also cheat a bit by moving the maximum and minimum frequencies in 10% or so from the band edges.

### Data Entry

As with all these programs, data must be entered in SI units. This means that it is up to you to enter the correct multiplier in all of the fields (p for pico, u for micro and so on.) If you get negative values for the trimmer and padder capacitors - ponder what it might mean!

 Enter Minimum Capacitance Cmin - F                 Enter Capacitor Swing - F                         Enter Minimum Frequency - Hz                      Enter Maximum Frequency - Hz                      Enter Intermediate frequency (i.f.) - Hz          Signal frequency Inductance L1 - Henrys            Oscillator frequency Inductance L2 - Henrys       Signal frequency trimmer Ct1 - F                  Oscillator frequency trimmer Ct2 - F              Padder capacitor Cp - F                           Median frequency used - Hz

The example provided (sample data) is for a typical medium wave superhet receiver. You might use 0-100pf trimmers and a 680pf silver mica padder capacitor. Note that for short wave bands, the padder will become larger and larger. At the same time, the bandwidth of the signal frequency circuits will also increase, so that for a simple radio, you may get away with no padder at all.  If you are building a "conventional" short wave superhet, then the ratio of highest frequency to lowest should be in the same proportion for each waveband. For example, if the lowest frequency range is 0.5 to 1MHz, then the ratio is 2:1. The next band would be 1 to 2 MHz, then 2 to 4, then 4 to 8, 8 to 16 and 16-32, giving 6 Wavebands. (As in the R390A signal circuits.) Some sets(e.g. AR88) "break rank" in order to provide greater bandspread on the high frequencies. (I think the AR88 uses a smaller value capacitor ganged to the main shaft. Anyhow, that's what it looks like.)

### The Theory

I'm just going to outline how it all works. Its really just a lot of messy algebra, which I couldn't be bothered to simplify, so I just threw it all ito the program "as is". You can look at the program by viewing the source in your browser.

Signal frequency:

\displaystyle{f={1\over {2\pi\sqrt{(L1(C+C_{t1}))}}}}
This gives us two unknowns, namely $L1$ and $C_{t1}$, and since we know the upper and lower frequency limits, we have two equations, which readily yield the answer. Now we know the signal frequency inductance and the trimmer value.

Median frequency:

We need to know this so that we can work backwards to calculate a median value for $C$, called $C_{med}$. Conventionally, this is the square root of the product of the upper and lower frequency bounds.

Oscillator circuit:

The frequency of the oscillator circuit is determined by the inductance of the oscillator coil $L2$ and the combination of $C$,$C_{t2}$ and$C_p$. This is given by:

\displaystyle{f={1\over {2\pi\sqrt{     {  {L2C_p(C+C_{t2})}\over {C_p+C_{t2}+ C}}  }}}}

We now have 3 frequencies, and three unknowns - $L2$, $C_p$ and $C_{t2}$. I did it by solving for $C_p+C_{t2}$, then the rest falls out fairly easily.

If you fiddle about with the above equations, you will see that at the low end frequency of the band, adjusting the trimmer makes only a small amount of diffrence - since it is a small proportion of the total capacitance of the tuned circuit. On the other hand, varying the inductance can make a huge change. The inductance can be varied over a 1.5:1 (or even 2:1) range if it has a ferrite core. (Make allowances for this if you are using ferrite cores). If you can't find inductances with ferrite cores, you will have to alter the inductance by winding and unwinding the coil or squeezing the turns. (Back to the future.)

At the high frequency end of the band, capacitance is to a very large extent made up by the trimmer, so this can easily set the top end of the band.

In some high-performance radios of a previous era, an aerial trimmer control is brought out to the front panel. This wasn't done on the Eddystone and Murphy B40 British radios, but my American sets all have front-panel trimmers, even if they don't really need them.

Modern radios either use a "wide open" front end (little or no coils) or tracking filters tuned by varicap diodes from a computer circuit.