If a receiving antenna and associated receiver circuits containing a simple rectifier are tuned to a continuous wave transmitter, the receiving telephone will be transversed by a uni-directional current and therefore the telephone emits no sound. But if by local means we cause the amplitude of these to fluctuate periodically at an audio frequency sound will be produced because the telephone diaphragm will be deflected at rates varying as the periodic fluctuations of the rectified current. Assume the antenna circuits are tuned to 8,000 meters, the oscillation frequency is 37,500 cycles per second and the local generated frequency is 36,500 cycles per second, the amplitude of the oscillations in the entire system will be varied from a maximum to a minimum at a rate due to the difference of 37,500 and 36,500 or 1,000 per second, i.e. the frequency of the "beat" currents will be 1,000 per second. These beats in turn are rectified by the detector and 1,000 pulses of direct current per second energize the telephone. The same beat frequency will be obtained if the local generated frequency is adjusted to 38,500 cycles per second; that is the frequency of the "beats" in every case equals the difference of the two applied frequencies. By changing the frequency of the local generated frequency, the receiving operator can change the pitch of the beat note from, say, 200 cycles to 1,000 cycles per second or beyond the limits of audibility. Not only can the note be varied according to the desire of the operator, but it can be shown that the efficiency of the receiver is thus increased, i.e., amplification of the incoming signal is secured.

The vacuum tube connected up for generation of radio frequency oscillations for the production of beat currents. This system is sometimes called the external heterodyne.
The grid and plate of the oscillation tube are magnetically coupled through the coil L; additional regenerative coupling is provided by condenser C. By proper selection of the values of L and C, the valve circuits will oscillate vigorously at any desired frequency. These oscillations interacting with the oscillations of the incoming signal produce beats in the detector circuits which in turn are detected by the valve.

The vacuum tube as a self-heterodyne or as a detector of continuous waves (Armstrong's Regenerative System).
The plate circuit is tuned to the incoming signal by L-3, C-3, P (C-2 may be fixed), and the grid circuit by L-2, S, C1. Usually a fixed capacity can be found for condenser C, approximately .00003 microfarad. Imagine any disturbance to occur in the plate circuit such as a sudden variation of the plate voltage - the resulting change of current through P causes it to act inductively on S, setting the grid circuit L-2, C-1, S, into oscillation. The grid then acts to vary the plate current at a radio frequency. Part of the plate circuit's energy is fed back to the grid circuit to keep the entire system in self oscillation. The frequency of the oscillations generated by the valve, will be approximately that of the grid circuit, if the capacity of the secondary condenser exceeds the capacity valve (grid to filament), but if it is less than the valve capacity, the inductance and capacity of the plate circuit will be the governing factor.
Let the valve circuits oscillate steadily and let the frequency differ slightly from the incoming signal; independently of the local oscillations the incoming oscillations change the grid potential, are repeated in the plate circuit and are reinforced in the grid circuit through the regenerative coupling M. Simultaneously these amplified oscillations interact with the local oscillations producing throughout the system the beats. That is, the amplitude of the repeated radio frequency plate current varies at an audio frequency.
As pointed out by Captain Armstrong, the great advantage of this system of reception lies in the fact that the telephones are transverse by an almost simple harmonic alternating current. Hence, the telephone receivers may be connected in a coupled audio frequency tuning circuit where selectivity or tuning independent of the signalling frequency may be secured.

Audio frequency tuning.

Audio frequency tuning circuit.

Two-step vacuum tube cascade amplifier. The grid circuit of the amplifying tube is tuned to audio frequencies.