Selectivity and voltage magnification
Through the application of positive feedback it is possible to greatly increase the apparent Q of an LC resonant circuit. This gives the LC circuit much greater frequency selectivity and a large voltage magnifying effect. You can use a Q multiplier to increase the selectivity of an IF filter in a superheterodyne radio circuit or as the basis of a regenerative receiver.
Figure 1 shows a Q multiplier based on the AC linked differential pair. The LC resonant circuit is comprised of L1 in series with L2 and the combined capacitance of C1,C2 and C4.
C1 and C2 form a capacitor tap that creates a suitable impedance match between the LC resonant circuit and the low input impedance present at the base of Q. It also greatly reduces frequency drift caused by variations in the base emitter junction capacitance which is a typical source of trouble. The amount of positive feedback is controlled by the voltage at the base of Q2. The positive feedback is injected as a current source signal through L2. The exact value of L2 is usually determined by experiment. The circuit in figure 1 has a compressive gain versus input signal response resulting in a smooth transition between the non-oscillating and oscillating states. In contrast the circuit in figure 2 has a slightly expansive gain versus input signal response. This results in it stepping over the transition zone between the non-oscillating and oscillating states by positive feedback hysteresis. Normally this would disbar a circuit from consideration. It has a number of compensating qualities that make it worth presenting though.
First, the very high capacitor tap ratio (C2,C3) results in an almost completely linear response to the voltage across the LC resonant circuit. Even a 1 volt signal across the LC circuit is reduced to 10 mV at the base of Q1 and the transistor amplifies small signals far more linearly than large signals. This allows you to get rather close to the transition zone between the non-oscillating and oscillating state, giving high selectivity and voltage magnification anyway. The simplicity of the circuit also results in very low (phase) noise which is a key limit with Q multipliers. You might ask how the circuit can work with such a high ratio reduction. The answer to that lies in transconductance of BJT transistors. At a collector current of 0.1 mA the transconductance of a BJT transistor is defined by the underlying physics as 4 mA per volt, at a collector current of 1mA it is 40 mA per volt, at a collector current current of 10 mA it is 400 mA per volt.
The amount of transconductance required in a Q multiplier is between 1 mA per volt and 10 mA per volt. Below 1 mA per volt the number turns on the inductor providing positive feedback to the LC resonant circuit becomes excessive and the finite output impedance of the amplifying device starts to load the LC resonant circuit. Above 10mA per volt providing the very weak coupling needed starts to become problematic. If you run a BJT with a collector current of 10 mA and put a 100:1 capacitor tap at the base the overall transconductance is reduced back to 4 mA and you get a lot of benefits in terms of high input impedance, low frequency drift and low phase noise.
A TRF radio application
Figure 3 shows an AM TRF radio circuit you can use with either of the Q multiplier circuits to create a regenerative radio. The TRF circuit is effective in itself and can enable you to listen to quite a few shortwave radio stations. To use it in conjunction with one of the Q multiplier circuits you need to replace the LC resonant circuit (L1,C6) with a few turns of wire placed in proximity to the LC resonant circuit of the Q multiplier. You also loosely couple an antenna to the Q multiplier LC circuit.
Unfortunately it is not possible for the Q multiplier circuit and the TRF circuit to share the LC resonant circuit, as even the minute currents flowing in the drain bend JFET detector are sufficient to disturb the delicate compressive/expansive properties of the sustaining amplifier in the Q multiplier. However there is a possibility that you could loosely couple the LC resonant circuit in the unmodified TRF circuit to the LC resonant circuit in the LC multiplier circuit to obtain a radio with a much higher ultimate rejection ratio than a simple regenerative radio circuit can provide. Of course you must be willing to deal with issues like frequency tracking 2 LC circuits if you want to do that.
Q multipliers are useful circuits that can provide superb performance with a few common components. They are also an area of manifest subtlety in circuit design where fine grained details have a large effect. The circuits above are tested and proven. Hopefully they will be of some use to you.