PHASE-COHERENT NARROW-BAND SIGNAL REGENERATION V. P. McGinn and M. W. Whitehead Department of Electrical Engineering Virginia Military Institute Lexington, Virginia 24450

KEY TERMS Coherence, filtering, phase locking, regeneration

ABSTRACT A phase-locked loop is combined with a highly selective bandpass filter in such a way that a steady-state single-frequency signal is extractedfrom a spectrum. The system goal is to maintain the phase of the wave irrespective of the actual signalfrrquency. 0 1995 John Wiley & Sons, Inc.

1. BACKGROUND Often it is necessary to use an extremely narrow bandpass filter to extract a specific steady-state signal from a spectrum of signals competing in amplitude. For example, a radar receiver may invoke synchronous detection methods if a carrier (reference) signal is available. Usually, however, this reference is embedded amongst other associated spectrum components. Thus, the requirement exists a pick out (or select) just the desired wave. Specifications for a filter of the required characteristics may be developed in eithcr the fre- quency domain or the time domain. Within the frequency domain it is not uncommon to specify the position of critical frequencies (poles and zeros) on the complex s plane, giving rise to familiar names such as Buttenvorth (a maximally flat in magnitude design), Chebyshev (sharper skirts but specified ripple in the passband), Bessel (linear phase) and others [9]. Also, it is possible to state desired amplitude versus fre- quency characteristics along with phase versus frequency characteristics. For any given design the two specifications are interrelated. Frequently, a filter quote is made regarding the - 3.0-dB (or - 6.0-dB) frequencies, the shape factor (this relates to the steepness of slope between the passband and the stop band), and how the phase of the wave will be altered as a frequency change occurs within the passband. Often, a linear phase characteristic is specified so as to avoid wave- shape distortion. This design imparts a constant delay to any signal within its passband. Regardless of filter type, however, signal phase alteration is inherent. This is a physical conse- quence of time delay accumulating as the wave proceeds through the filter. In order to achieve a narrow passband with steep transitions between stop band and passband the filter topology is necessarily sophisticated. As filter complexity in- creases, one expects greater variation in phase as frequency changes occur within the passband. Further time delays are imparted as more reactive (energy storage) elements are added. Unfortunately, a truly excellent filter with a narrow passband and steep transition slopes will impart a severe phase shift to the signal that it recovers. If the phase of this signal is important information for processing, filter phase bias must be eliminated.

II. FILTER TRACKING Exceptional signal selectivity in a microwave system is se- cured at the intermediate frequency (i.f.) of a heterodyne (signal-mixing) architecture. Therefore, this discussion will first confine itself to intermediate-frequency values. Figure 1

represents the amplitude and phase characteristics of a com- mercial filter. The designed response is of the linear phase variety. Notice that as frequency changes occur in the pass- band notable phase shifts occur at the filter output hut in a predictable fashion. The initial concept of compensation sug- gests that a second filter constructed to match the perfor- mance of the first be placed within the feedback path of a phase-locked loop (PLL). Thus, the output signal of the voltage-controlled oscillator (VCO) is in time synchronism (coherent) with the input wave prior to filtering. Figure 2 depicts the system embodying this concept. The reader will notice that the architecture is essentially the same as a conventional phase-locked loop with one exception: placed within the feedback path between the voltage controlled oscillator (VCO) and the phase comparator exists Filter 2. Thc electrical performance of this filter (amplitude and phase) matches that of thc primary filter (Filter 1). Filter 1 indeed has the desired amplitudc versus frequency characteristics; however, this filter is also imparting an undesired phase displacement to the original signal.

The basic constituents of a phase-locked loop encompass a voltage-controlled oscillator, a phase comparator, and a low-pass filter. In principle, the voltage-controlled oscillator will follow in frequency the incoming signal. With no incom- ing signal supplied to the phase-locked loop, the VCO oscil- lates at its free running or natural frequency. This alternating current (ac) signal is applied at the first input of the phase comparator. When an ac signal of sufficient amplitude is supplied to the second input of the phase comparator, lock occurs if the incoming signal is within the capture range of the system. If it so happens that the incoming signal fre- quency is the free-running frequency of the VCO then no error-correcting signal extends past the low-pass filter. This condition corresponds to the two comparator input signals possessing a specific phase relationship (it will be 0" or 90" depending on system design).

If the input signal to the phase-locked loop is changed in frequency a zero-frequency (dc) error signal is developed at the output of the low-pass filter. This signal properly corrects the VCO frequency, thus maintaining lock. However, now the phase difference between the two signals supplied to the phase comparator is changed from 0 (or 90) degrees. Signal capture only exists between asymptotic phase limits of + 90.0 to - 90.0 (or 0.0 and + 180.0) degrees. Conventional phase- locked loop design goals establish the capture range, This specification is intimately linked to loop speed of response and dynamic phase accuracy.

If the passband region of Filter 1 (and Filter 2) is signifi- cantly smaller than the capture range for the phase-locked loop then the regenerated signal output mimics the frequency component that we wish to filter out from a broad spectrum with only a slight departure in phase from that original component. For example, in a system that was examined it was noted that (at the central frequency of the lock region) phase sensitivity corresponded to 50.0" per megahertz, How- ever, Filters l and 2 restricted system operation to signal components between the frequencies of 20.023 and 20.037 MHz. Thus, the total maximum phase error of the regener- ated signal is calculated:

(20.037 - 20.023) MHz X SO.O"/MHz = 0.7".

The maximum positive (or negative) phase error (devia- tion) corresponds to half this value. That is, the regenerated

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 8, No. 6, April 20 1995 273

DECIBELS

-10.0

O . 1

I E&E=L4TBJ

- 2 0 . 0

AMPLITUDE \

20.024 20.028 20.028 20.030 20.032 20.034 20.038

Figure 1 Filter characteristics

SIGNAL - FILTER 1 INPUT

r FILTER2

signal output will be within +0.35" of the original compo- nent. This performance is exceptional when one realizes that for this investigation Filter I and Filter 2 each utilize eight complex poles. Of course, if the filters are not matched this performance may not be realized in practice. The laboratory investigation undertaken for this effort revealed phase match- ing to better than k0.5".

Usually, the intermediate frequency (i.f.1 results from a mix down between the microwave carrier frequency and a microwave signal from a local oscillator (LO). Obviously, very narrow-band filtering demands exceptional frequency stability of both sources.

To regenerate the original microwave carrier signal the same local oscillator must be used to mix up the regenerated i.f. signal from the phase-locked loop. Phase coherence is maintained with the translator subsystem depicted in Figure 3. Careful design attention to the mixers (MIX) is necessary to maintain image suppression. Further, the mixers must impart little additional phase shift.

111. SIGNAL-FILTER TRACKING In many applications, narrow system bandwidths as described in the previous section may not be required and may even be undesirable. Within this discussion the phrase narrow band- widths refers to spectrum space that is a few percent (or less)

t - 400.0

I

- 200.0

- 0.0

- -200.0

- -400.0

INPUT n MICROWAVE 7 ;" ] TOFILTERTRACKINGPU

SIGNAL

I

Figure 3 Signal Translator

of a mean frequency value located within the passband. In such cases filtering within the original radio frequency (rf) band is entirely feasible. Also, it is recognized that matching (and maintaining) electrical characteristics of two filters of sophisticated design may prove difficult. Present investiga- tions have yielded most encouraging results with the use of one filter only. The proposition is to use the same filter to match itself in compensation. Such a technique demands that the filter be a reciprocal and bilateral network. In terms of open-circuit impedance parameters [ Z ] the first requirement (reciprocity) is met with zI2 = zZ1. The bilateral requirement is established with zll = zZ2 [Z]. Then, the feed-forward char- acteristic of the filter is compensated by the feed-reverse characteristic of the same filter. In Figure 4 it is noted that both the input and the output of the filter are terminated in hybrid (H) networks (or directional couplers). Then, the sig- nal at A is the original but phase-shifted (by Filter 1) signal in the feed-forward direction. This is matched at the phase comparator by the signal at B, which extends from the VCO but is phase shifted (by Filter 1) in the feed-reverse direction. The hybrid networks must not introduce unpredictable or excessive phase shift [31.

274 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 8, No. 6, April 20 1995

SIGNAL >- . IN

/

B

, SffiNAL arr

PHASE

FILTER

Figure 4 Single-filter compensation

SIGNAL

SIGNAL CVI

Figure 5 Heterodyne single-filter compensation

It is interesting to note that the single-filter compensation method may be embedded in a heterodyne topology. In order to maintain coherence it is required to utilize the same local oscillator (LO) signal in the feed forward and feed reverse mixers (MIX). This is shown in Figure 5. The system in Figure 5 should prove useful in situations requiring relaxed phase comparator characteristics. This system allows the usc of a low-frequency phase comparator. l T L and CMOS logic have been used successfully in the phase comparison func- tion.

IV. SUMMARY

Narrow-band filters have established the bandpass character- istics of the subsystems outlined. Therefore, the frequency capture range of the PLL is always much wider (orders of magnitude) than the pass band of this filter. Because the filter specifications include its transfer function, system de- sign reverts to established PLL design principles. This article is intended to provide a quick report on the topology of this technique only. Specific performance is peculiar to the in- tended application.

ACKNOWLEDGMENTS Much thanks for discussions supporting this report are due to our friend and colleague M. D. Antony. Additionally, the authors wish to recognize Dr. M. S. McGinn for her support.

REFERENCES 1. R. Bddessa, “A Communications Detector with a Signal-Synthe-

sized Reference,” IEEE Trans. Commun. Technul., Vol. COM-19,

2. R. S. Elliot, An Introduction to Guided Waues and Microwave Circuits, Prentice Hall, Englewood Cliffs, NJ, 1993.

3. G. L. Mattaei, L. Young, and E. M. T. Jones, Microwaiw Filters, Impedance Matching Nelworks and Cuupling Structures, Artech House, Norwood, MA, 1980.

NO. 5, Oct. 1971, pp. 643-648.

4. Schwartz, M., Informution, Transmission, Modulation, and Noise (4th ed.), McGraw-Hill, New York, 1990.

5 . M. Tam, M. H. White, and Z. Ma, “Theoretical Analysis of a Coherent Phase Synchronous Oscillator,” IEEE Trans. Circuits Syst., Vol. CAS-39, No. 1, Jan. 1992, pp. 11-17.

6. V. Uzunoglu, “Coherent Phase-Lacked Synchronous Oscillator,” Electron. Lett., Vol. 22, No. 20, Sept. 25, 1986, pp. 1060-1061.

7. V. Uzunoglu and M. H. White, “The Synchronous Oscillator: A Synchronization and Tracking Network,” IEEE J . Solid State Circuits, Vol. SC-20, No. 6, Dec. 1985, pp. 1214-1226.

8. V. Uzunoglu and M. H. White, “Synchronous and the Coherent Phase-Locked Synchronous Oscillators: New Techniques in Syn- chronization and Tracking,” IEEE Trans. Circuits Syst., Vol. 36, NO. 7, July 1989, pp. 997-1004.

9. A. I. Zvrev, Handbook of Filter Synthesis, Wiley, New York, 1967.

Received 9-6-94; revised 11-11-94

Microwave and Optical Technology Letters, 8/6,273-275 0 1995 John Wiley & Sons, Inc. CCC 0895-2477/95

QUASIOPTICAL SMMW RESONATOR WITH EXTREMELY HIGH Q FACTOR Dominik Steup Laboratories for High Frequency Technology University of Erlangen - Nurnberg 0-91058 Erlangen, Cauerstrasse 9 Germany

KEY TERMS Quasioptical resonator, Gauvsian optic.s, Q-factor measurements

ABSTRACT A quusioptical resonator for the frequency range between 170 and 260 GHz and a Q factor of more than 50,000 has been built. We use a serniconfocal resonator that is tunable in resonance and has a passice temperature stabilization. 7he coupling in of electromagnetic energy is realized using metallic meshes with quadratic apertures and polarizing wire grids as well. The resonatur is tuned by inuring the spherical mhor with a piezo driuer. 0 I995 John Wiley & Sons, Inc.

1. INTRODUCTION

In the millimeter- and submillimeter-wave ranges quasiopti- cal resonators are widely used in various measurement se- tups. In principle they are applied for shaping a purely Gaussian beam profile, for highly precise frequency measure- ments, and other interferometric applications.

For extremely sensitive and precise measurements a res- onator having a high quality factor is necessary. In hollow waveguide resonators this quality factor strictly decreases according to 1/ fi if frequency is increased [l]. This is valid for each mode in a closed cavity. Therefore, at higher fre- quencies in the submillimeter-wave range the quality of wave- guide cavities becomes too poor for effective measurement systems to be built. The small dimensions render the fabrica- tion of waveguide cavities at submillimeter-wave frequencies more difficult.

Because of these problems quasioptical resonators repre- sent a practical solution from the millimeter-wave to the optical frequency range. They have hardly any ohmic loss and their dimensions are in the centimeter range, but they have the disadvantages of rnultimode operation and low thermal

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