## Doug Adams June 10, 2012

### Submitted as coursework for PH250, Stanford University, Spring 2012

 Fig. 1: Schematic of a characteristic regenerative radio receiver. Source: Wikimedia Commons. Fig. 2: The effect of successive passes through the positive feedback loop on the transfer function of the receiver.

## Introduction

The regenerative radio was developed by Edwin H. Armstrong and patented in 1914. [1] The receiver uses a single vacuum tube for both amplification and detection, utilizing positive feedback to both increase the gain from a single vacuum tube and to improve the selectivity of the receiver. [2]

## How it Works

A schematic of the regenerative receiver is provided in Fig. 1. It works as follows. The incoming RF signal is taken from the antenna and passed through a tunable band-pass filter tank so as to select the desired channel. That signal is then amplified by a triode or other device. The amplifier's output signal is then fed back into the resonant tank via the tickler coil where it is once again filtered by the tank and amplified by the tube. [2] The reuse of the same vacuum tube through the positive feedback loop greatly increases the gain of the system, providing incredibly high gain which would be otherwise unattainable with a single tube. The two effects of positive feedback--increased in gain and bandwidth sharpening--are easily understood through simplified analysis of the system. Consider the series of transfer functions depicted in Fig. 2. Without positive feedback the circuit has the transfer function depicted by the blue curve. With positive feedback enabled the signal is passed through the circuit multiple times, each pass increasing the selectivity of the filter and the passband gain of the receiver. The passband gain and the selectivity of the circuit system are both extremely high, but remain finite as a result of diminishing returns in the feedback loop. The exact mathematical description of this system is outside the scope of this report.

 Fig. 3: Applying even order distortion to the AM signal and low pass filtering the result effectively demodulates the desired signal

The nonlinear response of the single vacuum tube is also used to demodulate the signal. [2] Fig. 3 demonstrates this effect. The original AM signal is passed through the distorting nonlinearity of the tube, which applies different levels of distortion to positive and negative swinging signals. Sending this distorted signal through a simple low pass filter is enough to recover the desired signal.

## Problems with the Regenerative Receiver

Despite its fantastically clever design, the regenerative receiver lost out to other receiver topologies in the 1930s. [3] When operating the regenerative receiver it is necessary to properly select the amount of positive feedback to apply to the system; too little and there is not enough gain or selectivity to properly receive the signal, too much and the positive feedback will cause the entire circuit to oscillate. When oscillating, not only is it impossible to receive any signal with the device, but those oscillations will be driven against the antenna and reradiated into the air. Any nearby receivers attempting to tune to the same channel will be saturated by those oscillations. Despite this shortcoming, regenerative receivers are still used in systems where the benefits of a more robust topology do not offset the costs incurred by the additional components.

© Doug Adams. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

## References

[1] E. H. Armstrong, "Wireless Receiving System," US Pat. No. 1,113,149, 6 Oct 14.

[2] E. H. Armstrong, "Some Recent Developments in the Audion Receiver," Proc. Inst. Radio Eng. 3, 215 (1915).

[3] T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits (Cambridge, 1988), p. 13.