Next in the series of 'How not to design transmitters and receivers' we shall tackle the intermediate (IF) amplifier. This seemingly innocent little circuit is teeming with complexity and getting it right is not straightforward.

According to the calculations made in Part 15 of this series, the IF amplifier requires a gain of 19 dB or thereabouts (a few dB or so either way will not make too much difference). In addition, it needs to have an input and output impedance of 330 Ohms. This means that any ceramic filter used in the IF could be placed either before, or after, the amplifier and be correctly matched (or indeed two filters could be used). It is the combination of achieving a 330 Ohm input and output impedance, together with the requisite gain that makes the circuit more complex.



We shall use the circuit above as the basis for our amplifier. This is an untuned amplifier and will therefore provide gain across a wide range of frequencies which can sometimes cause problems as it will amplify both wanted and unwanted signals, however this has the major advantage that no tuning is required.

The gain of the circuit is primarily set by the ratio of Rc and Re, with gain being calculated as Rc divided by Re. However it needs to be remembered that Rc is in parallel with the load connected to the output, and that the transistor has an internal resistance in series with Re whose value is determined by the current flowing through the transistor (usually defined as 26 divided by the transistor emitter current (I_e in milliAmps).

Taking all this into account, the gain of the circuit can be (roughly) calculated by the equation:

Rc*R_load
(Rc+R_load)*(Re+26/I_e)

Note that this circuit also has additional negative feedback (via Rf) which will also impact (reduce) the gain, depending on the input impedance feeding the amplifier. The gain in this case will never exceed Rf/R_input. This effect will be marginal as long as the value of Rf is far above that of the input impedance of the circuit. As we are aiming for an input impedance of 330 Ohms, something over 10,000 Ohms (10K Ohms) will have only a small impact. Nevertheless, we should aim for the gain calculation above to produce a result slightly higher than that which we are aiming to achieve overall.

The input impedance of the circuit comprises three different values in parallel:

• Rb which is directly across the input of the circuit;
• The impedance of the emitter resistor Re (including the transistor's internal resistance) multiplied by the gain of the transistor (the Beta or h_fe); and
• The impedance of the feedback resistor Rf divided by the gain of the transistor circuit (not the gain of the transitor itself).

The input impedance of the amplifier can thus be calculated by the equation:

1
1/Rb+1/(h_fe*(Re+26/I_e))+1/(Rf/gain_circuit)

The output impedance of the amplifier is composed of the impedance presented by the transistor in parallel with Rc. The impedance presented by the transistor is approximately equal to the voltage between the collector and emitter divided by the current passing through the transistor. The output impedance of the amplifier can be calculated by the following equation, where V_cc is the voltage of the power supply:

Rc*(V_cc-Rc*I_e)
V_cc

This holds true as long as Rf is substantially larger than Rc.

One final consideration is the transistor bias. Ideally, the output of the transistor would be set to have a voltage roughly half of that of the supply (give or take). This ensures that the output of the amplifier can swing up and down as far as possible before 'hitting the rails' and no longer amplifying. The output voltage (at the transistor's collector) is determined by Rc and the current passing through the transistor. The current passing through the transistor is determined by the current flowing into the base of the transistor multiplied by its gain. In the case where the bias current is set through the feedback resistor from the collector (Rf), this calculation is iterative, as the base current is then related to the collector current.

Another kink is that the collector current can also impact the gain of the transistor, with very low collector currents reducing the gain. Similarly, currents too high can have similar effects. It is necessary to consult the datasheet for the transistor being used to determine how the current affects the gain. Usually over a relatively wide range, the gain will be roughly constant (and be at its highest) and this is often the point that should be aimed for.

Hopefully, by now, you can see why getting the various resistor values correct is complicated, and how changing one value (such as the emitter resistor, or feedback resistor) can change the gain and impedances of the circuit.

The following values therefore produce an amplifier which meets, so far as is possible, all the criteria which are required for the IF gain stage:

• Rb = 2.2K Ohms
• Rc = 560 Ohms
• Re = 8.2 Ohms
• Rf = 10K Ohms

Using these values, the collector current is roughly 7.5 mA meaning that the voltage at the collector, assuming a 9V supply, would be 4.7 Volts (i.e. giving the output a large peak-to-peak swing before hitting saturation). Knowing that the h_fe of the transistor at this current is approximately 110, and using the equations provided above, you should be able to confirm the fact that:

• The voltage gain of the amplifier is 17.8 (or 25 dB) before the reduction in gain caused by the feedback resistor Rf is taken into account;
• The input impedance of the amplifier is 331 Ohms;
• The output impedance of the amplifier is 299 Ohms.

These are well within the range that we are trying to achieve and so will 'do the job nicely'.

Another set of values which yields the correct input and output impedances is:

• Rb = 1K Ohms
• Rc = 470 Ohms
• Re = 22 Ohms
• Rf = 4.7K Ohms

In traditional academic style, and armed with the knowledge that the collector current in this example would be 5.5 mA, it is left to the reader to do the maths and work out what the gain and input and output impedance would be.

Note that in reality there are various additional factors which will impact the performance of the circuit, especially at radio frequencies. In particular, various capacitances within the transistor will tend to limit the high frequency performance. Choosing a transistor whose transition frequency (f_t - the frequency at which the transistor's gain drops to unity) is significantly above the required amplifier frequency minimises these issues. According to its datasheet, the 2N3904 used in the amplifier has an (f_t) of 300 MHz, and as we want the amplifier to operate at 10.7 MHz, this is sufficient margin to largely ignore these other factors.