Pulsed signals are commonly employed in military systems, most notably in radar transmitters and receivers. Understanding a receiver’s response to a pulse-modulated carrier can help predict its behavior when working with different types of transient signals, especially when the input signal is at a frequency that is offset from the tuned response of the receiver. Because the bandwidth of a pulse-modulated input signal can often exceed the tuned response of a receiver and its signal-processing components, such as filters, it is important to anticipate the appearance of the receiver’s output waveforms under such conditions.

Tests run on receivers with pulse-modulated carriers of arbitrary frequency have commonly produced a “rabbit-ear” response at the receiver’s output as the input frequency was offset from the receiver’s tuned frequency. The receiver’s output response consisted of transients at the leading and trailing edges of the waveform; the center portion of the waveform was at the frequency of the input signal. The transients were at the natural frequency of the receiver’s tuned network.

As the input signal was further detuned from the receiver, the peaks at the beginning and end of the waveform remained constant, but the amplitude of the center portion decreased further with detuning. This phenomenon occurs when the pulse width of the carrier is more than twice the reciprocal of the receiver’s filter bandwidth. These tests were run on signals with decreasing and increasing offset frequencies, as well as with video pulses. For a video pulse with positive input, the receiver’s output waveform had an impulse-like response at the leading edge of the waveform, starting in a negative direction, with an impulse-like response at the trailing edge of the input pulse starting in a positive direction.

In 1935, E. A. Guillemin analyzed the response of an ideal bandpass filter to a suddenly applied substantially detuned pulsed sinusoidal waveform.1 The response to the input signal appeared to be the impulse response of the filter. During the 1940s, researchers at the Massachusetts Institute of Technology (MIT) Radiation Laboratory2 observed that the response of a tuned intermediate-frequency (IF) amplifier showed what is commonly termed as rabbit ears—when a detuned pulse-modulated carrier signal was applied.

During a 1966 study on the off-tuned responses of RF field intensity meters, Caprio rediscovered the phenomenon of rabbit ears and noted it occurred for detuned signals both above and below the tuned frequency of the bandpass network.3 In March 1968, A. K. Smolinski published a report with equations similar to those of Caprio’s.4 This phenomenon occurs when the pulse width of the carrier is greater than twice the reciprocal of the filter bandwidth. An experiment was conducted on a five-stage synchronously tuned IF module with a tuned frequency of 30.24 MHz. It was observed that, as the input signal was tuned further from the tuned frequency, the peaks at the beginning and end of the output waveform remained essentially constant while the amplitude of the center portion of the waveform decreased the further the input was detuned. It was noted that the central portion of the waveform was attenuated by an amount equal to the attenuation of the module at the input frequency. This attenuation was equal to the value that would be measured for a CW signal at the offset frequency.

An analysis was conducted for an N-stage synchronously tuned IF module to determine the response to a detuned pulse modulated signal. The assumption had been that even with such signals, the receiver would operate in its linear range, with its mixer providing ideal frequency translation. The module was tested on its own to better understand the IF network’s behavior to such signals. Predicted results were compared to tests of a five-stage synchronously-tuned IF module at various offset frequencies and verified the measured results. Tests were conducted with decreasing offset frequencies and with video pulses, as well as with increasing offset frequencies. For a positive input video pulse, the output waveform had an impulse like response at the leading edge of the waveform starting in a negative direction and an impulse-like response at the trailing edge of input pulse starting in a positive direction.

Reverse polarities occurred for a negative pulse. The magnitude of the leading-edge response increased as the rise time of the input pulse decreased. The peak of the trailing edge of the response was also noted to increase (become more negative) as the fall time of the input pulse decreased. The observed time responses appeared to be the impulse response of the module.

In 1980, Caprio5 showed that the responses of AN/PRM-25 (XN-1) and AN/PRM-27 field intensity meters were identical for either an impulse signal from a commercial signal generator or a video pulse, but the phase responses of the waveforms were different. The phase shift for a true impulse response has a phase shift equal to N times the phase shift of one stage. The response of the IF module to a video pulse has a phase shift of (N-1) times the phase shift of a single stage. In 1986, J. P. Hanson of the Naval Research Laboratories (NRL) used 45-ps rise-time voltage pulses from a time-domain-reflectometer (TDR) pulse generator to directly drive a microwave transmit amplifier.6 The transmitted signal was used for high-resolution measurements of the backscatter from splashes.

Receiver IF modules can be categorized into three general classes:

1. N-pole (or N-stage) synchronously tuned IF module, where the voltage-transfer function (gain) of the module has Nth-order poles.
2. Maximally flat (Butterworth) amp-lifiers, where the voltage transfer function of the module is stagger tuned. The amplifier stages are designed so the N poles of the transfer function lie on a semicircle in the complex frequency plan with the center at the resonant frequency of the amplifier.
3. Over-staggered (Chebyshev) amplifiers, where the stages are designed so the N poles of the transfer function lie on a semi-ellipse in the complex frequency plane with the center at the resonant frequency of the amplifier.

This study only considered the off-tuned response of an N-stage synchronously-tuned IF module. The wisdom of this choice may be questioned since few wide-band receivers for pulse modulated signals use synchronously-tuned IF amplifiers. Of the three classes of IF amplifier module, the synchronously tuned IF amplifier has the smallest gain-bandwidth product.

Appendix A presents derivation of the weighting function (impulse res-ponse) for an N-stage synch-ronously-tuned IF module given by equation A-15 (eq. 1 in this article). Appendix B presents the response of an N-stage synchronously-tuned IF module to a pulse modulated carrier signal at an arbitrary frequency given by equation B-6 (eq. 2).

The general response consists of the following three terms:

1. An attenuated and phase-shifted replica of the input pulse;
2. Leading-edge transient responses at the natural frequency response of the IF module; and
3. Trailing-edge transient responses at the natural frequency response of the IF module.

Appendix B presents the response of N-stage synchronously-tuned IF module to a pulse modulated carrier. Equation B-6 presents the response of N-stage synchronously-tuned IF module to a pulse modulated carrier of arbitrary frequency. Equation B-7 shows the leading edge response of the IF module, assuming the video pulse width is much greater than the reciprocal of the overall bandwidth of the module. Appendices A and B are not included in this article, but electronic copies may be requested from the author by addressing an e-mail request to sjcaprio@comcast.net. The response of the IF module is given by eqs. 1 and 2, shown in the box below. If u = t/2RC, then the response of an N-stage, synchronously tuned IF module to a video pulse is defined by the expression for e0(t) in Eq. 1 for N stages and by the expression in Eq. 2 for e0(t) as a sum of exponentials. These equations originally appeared as equations in an Appendix to another work published by the author.

If ô >> 1/RC, eq. 2 indicates that the response reduces to an attenuated impulse response at the leading edge and trailing edge of the input video pulse.

Figure 1 shows the CW selectivity of a five-stage synchronously tuned IF amplifier. Figure 2 shows the response of the IF mocdule to a tuned pulse-modulated signal at 30.24 MHz. Figure 3 shows the predicted leading-edge response of the IF module to a pulse-modulated signal at 25.54 MHz. Figure 4 shows that the predicted leading-edge response of the IF module to a positive video pulse. The peak transient response is about 6.8 dB greater than the steady-state response. Figure 5 shows the block diagram of the equipment used to generate a phase-coherent UWB signal using a video pulse and the waveform with a center frequency of 1.1 GHz. Figure 6 shows the leading edge of the generated waveform.

The results of the study illustrate the effects of the response of tuned devices, such as radio receivers and filters, to pulse-modulated signals of arbitrary frequencies. It also illustrates that a coherent waveform can be generated by a tuned bandpass network.

The problem with this technique, however, is the capability of maintaining the frequency stability of the filter’s natu-ral frequency and the frequency stability of the receiver’s active components, which are sensitive to changes in frequency as a function of changes in temperature. One solution is to package the components in an oven-controlled module.

References

1. E. A. Guillemin, Communication Networks, Wiley, New York, 1931, pp 488-489.
2. George E. Valley, Jr. and Henry Wallman, Vacuum Tube Amplifiers, Vol. 18 of MIT Radiation Laboratory Series, McGraw-Hill, New York, 1948.
3. S. J. Caprio, “Investigation of Off-Tuned Response of RF Field Intensity Meters,” BuShips Problem 65-17, Phase V, Dated July 1966; NANEP Branch, Naval Electronics System Command.
4. A. K. Smolnski, “High-Frequency Pulse in Synchronous Six-Stage Single-Circuit Amplifiers,” IEEE Transactions on Circuit Theory, March 1968, pp. 94-97.
5. S. J. Caprio, “Comparison of the response of a Heterodyne Receiver to Video-Pulse and Impulse-Type Signals,” IEEE Transactions on Electromagnetic Compatibility, Vol. EMC-22, No. 1, pp. 68-72.
6. J. P. Hansen, “A System for Performing Ultra High Resolution Backscatter Measurements of Splashes,” 1988 IEEE MTT-S Digest, pp. 633-636.