RF/Microwave SAW Modules

Pulse Compression

Radar’s range is determined in part by its radiated pulse length T, and its resolution is determined by its radiated bandwidth B. But in simple systems, B*T=1, which means that good range and resolution are mutually exclusive.

Pulse compression is a method of breaking this unwanted constraint between range and resolution. Pulse compression radar transmits a modulated pulse which is both long (i.e. good range) and wideband (i.e. good resolution). The pulse compression receiver compresses the long received signal of length T into a short signal of width 1/B. It does this by delaying each sub-part of the input signal spectrum different amounts so that each sub-part arrives at the output at the same instant. The pulse compression ratio is T/(1/B) or B*T.

Matched Filtering is a generalization of pulse compression which states that given a received signal s(t) and spectrum S(f), the Matched Filter is that receiver filter which maximizes the output signal to noise ratio, and it has impulse response s(-t) and frequency response conjugate(S(f)).

Pulse compression subsystems consist of a transmitter waveform generator IF module, either digital or based on a gated limited SAW impulse response,  and a unity gain matched filter receiver IF module. A matched filter may give sidelobes so large that they mask a small target in the presence of a large target, so the receiver is often purposely mismatched for sidelobe suppression. Receivers can also have multiple amplitude &/or phase matched &/or tracking channels.

There are several types of pulse compression identified by the modulation used on the transmitted pulse:

LINEAR FREQUENCY MODULATION (LFM) was the earliest and is still the most common type of pulse compression. A LFM Dispersive Filter with flat impulse response is used for the generation of the transmitted pulse. A LFM Dispersive Filter with opposite chirp rate is used in the pulse compression receiver, which is usually mismatched for sidelobe suppression by adding Taylor or Hamming amplitude weighting to the frequency response, at the cost of typically 50% pulse broadening and 1.5 dB signal/noise loss.

NON-LINEAR FREQUENCY MODULATION (NLFM) is used when the mis-matched LFM filter with its attendant pulse broadening and signal/noise loss is unacceptable. The NLFM receiver is a true matched filter. The price is Doppler sensitivity: the maximum allowed Doppler is approximately .1/T.

PSEUDO-RANDOM NOISE MODULATION (PN) is used when FM will not meet system requirements. A SAW matched filter receiver may be used, but sidelobes and Doppler sensitivity are generally large.

Spectrum Analysis

 The resulting subsystems can process in real time at rates far in excess of current digital techniques, with relatively little size, weight, and power. Applications include ELINT, COMINT, RWRs, Laser Radar Doppler Processors, and advanced communications techniques.

Mathematical Foundations

Consider the Fourier transform S(f) of a signal s(t) which is bandlimited to B and of maximum duration T. The Fourier transform integral is easily rewritten in the form of the “chirp transform algorithm”:

		S(f)=S(at)=((s(t).R1(t))*R2(t)).R1(t)

				    M      C      M

where . is multiplication, * is convolution, a=B/T is the scale factor, R1(t) is the impulse response of a DDL of length T with chirp rate -a, and R2(t) is the impulse response of a DDL of length 2T with chirp rate a.

The expression for S(at) shows that the sequence of operations on s(t) are: Multiply by a LFM pulse, Convolve by a DDL, Multiply by a LFM pulse. This is the MCM operator.

The dual CMC operator may be derived using the convolution theorem:

		S(f)=S(-at)=((s(t)*R1(t)).R2(t))*R1(t)

				   C       M       C

Realization Considerations

POI: The finite duration of R1(t) and R2(t) allow the processing of a T time “frame”. With a system trigger rate of 1/T, the “frames” are contiguous so that a 100% Probability of Intercept (POI) is obtained.

Weighting: For CW input, the processed output is a sinc of -4dB width 1/T, so BT discrete frequencies are resolved over B. For applications with quasi-stationary inputs it is possible and desirable to weight the system to replace the sinc (-13dB sidelobes) output with a Taylor (-35dB sidelobes) output at the cost of a 1.5 resolution reduction. MCM weighting is introduced in time at the first M, and CMC weighting in frequency at the last C.

Multiply: In the unweighted case, the M operators can be realized by doubly balanced mixers with R1(t) and R2(t) as constant level LOs. For weighted MCM, weighting must be introduced thru bilinear multiplication at M1. For weighted CMC with 100% POI, two M operators must be time multiplexed so that concurrent LOs do not produce undesirable intermodulation products.

Multi-Channel Processing: Multiple processor channels may share common M operator LOs, and their DDLs may be thermally stabilized in a common oven. This commonality enhances coherence and tracking accuracy.

From these considerations arise the four common processors described below. They are identified by their operators with any deleted operations enclosed in parentheses:

• MCM: for unweighted 100% POI Fourier transformation applications, weighting requires bilinear multiplication.
• MC(M): for unweighted 100% POI spectrum analysis applications, where the output phase is unused. Multi-channel differential phase is the same as MCM.
• CMC: for weighted 50% POI Fourier transformation applications. 100% POI is achieved by multiplexing two M operators.
• (C)MC: for weighted <=50% POI spectrum analysis applications, where output phase is unused. Multi-channel differential phase is the same as CMC.

A frequency time-plan for the CMC configuration is shown above. The BT input domain is convolved into the M input domain, mixed with the M LO to obtain the M output domain, and then convolved into the TB output domain. To define the domain boundaries and interior examples, CW signals are represented by solid lines, and impulses by dashed lines. Note that the output domain is simply the input domain with f=(-B/T)t, as stated by the mathematical formulation. For 50% POI simply retrigger (i. e. replicate) the plan at 2T intervals.

Digital Sources

• Arbitrary FM Waveform Generation by DDS plus Piece Wise Linear with compact waveform description
• FPGA+DAC based, sampling to 3.2GHz, optional quadrature modulator
• Bandwidth to 1GHz
• Pulse lengths effectively unlimited
• Multi-Waveforms, fast programmable
• Continuous temperature compensation, fast programmable
• Inputs: LVTL CLK, LVTL Trigger, single voltage power, serial programming interface
• Militarized package, -40C to 85C

Key to Abbreviations

Material Code

STQ = 42.75 degree rotated Y cut, X propagating, SiO2, Temp Coeff = 3E-8

##YX-Q = 32 to 43 degree rotated Y cut, X propagating, SiO2, Temp Coeff = 3E-8

YZ-LN = Y cut, X propagating, LiNbO3, Temp Coeff = 94E-6

128YX-LN = 128 degree rotated Y cut, X propagating, LiNbO3, Temp Coeff = 75E-6

X112Y-LT = X cut, 112 degree from Y propagating, LiTaO3, Temp Coeff = 18E-6

Matching Code

external matching elements listed from source to load

series elements upper case, shunt elements lower case

R=resistor, L=inductor, C=capacitor, T=transformer, B=balun, S=saw

Z = internal impedance match

C = connectorized

O = ovenized

A = amplified

S = switched

M = multiplexed

W = weighted amplitude

# = used in module p/n #, or uses component p/n #, with hyperlink to that p/n

Notes:

1. A Component is a hermetic SAW product with no DC connections
2. A Module contains one or more Components
3. A Subsystem contains multiple Modules
4. Spurious is in the time domain. The principle spurious are feedthru and triple transit. ‘NA’ is designated in this column for Resonators in the Bandpass Filters section.
5. ITAR unrestricted parts in standard packages, indicated by asterisks to the right of the Model numbers below, are available for web sale in small quantities.

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