Dispersive Filters

Overview

Dispersive Filters (DF), also called Dispersive Delay Lines (DDL), are linear filters with group delay that varies by T over their passband B. In other words, the impulse response of a DF is an FM pulse whose instantaneous frequency varies by B over its duration T. The FM is usually chosen to be linear (LFM), with the amplitude response being flat or weighted to suppress sidelobes. Nonlinear FM (NLFM) can also be implemented, the tradeoff being improved signal to noise versus greater Doppler sensitivity. Several techniques are available to manufacture such filters. All consist in varying the propagation path length with frequency.

Interdigital Dispersive (ID) Filters

This technique includes the dispersion effect one or both transducers on a quartz or lithium niobate substrate. The transducer is then composed of a great number of electrodes whose effective periodicity varies from one extremity to the other. As with bandpass filters, position and length of the electrodes set the phase and amplitude of the response. With in-line transducers, BT to 500 are possible. With slanted transducers, BT to 12000 and post-photolithography phase error correction are possible.

Reflective Dispersive (RD) Filters

The RD, also called RAC or Reflective Array Compressor, is the dominant LFM DF technique for large T. It uses a quartz or lithium niobate substrate (usually heated) with short transducers and obtains dispersion with two long oblique acoustic reflector arrays which are frequency selective due to their non-uniform period. The reflectors are metal deposited at the same time as the transducers. The RAC allows post-photolithography phase error correction by insertion of a metallic film pattern between the arrays.

DF Performance

Product Code:	ID	RD
Bandwidth B MHz	1000	500
Dispersion T us	25	100
BT	12000	12000
Center frequency MHz	1500	1500
Relative bandwidth %	150	60
Sidelobes dB	30-40	30-40
Insertion loss dB	20-40	30-50

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:

A Component is a hermetic SAW product with no DC connections
A Module contains one or more Components
A Subsystem contains multiple Modules
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.
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.

Specifying a Dispersive Filter

1. Do not specify and tolerance the PassBand center frequency and bandwidth, instead define without tolerance the center Fo and width B of the PassBand in which other parameters are specified.
2. Specify the minimum insertion loss in the defined PassBand.
3. Do not specify passband amplitude or phase ripple. If amplitude is weighted then reference the ideal weighting function (e.g. Taylor 40dB 100MHz). Specify instead the key output compressed pulse characteristics: pulse width, sidelobes and s/n mismatch loss. If max noise band width is important then specify it.
4. If an expander, specify the impulse response pp amplitude flatness inside a defined interval of width T centered at T0, and the subsequent compressed pulse response of an ideal compressor.
If a compressor, specify the compressed pulse response for an ideal rectangular FM input of width T centered at t=0, and chirp rate T/B us/MHz or an analytic expression for phase(t).
5. Specify the compressed pulse at zero doppler:

maximum -3dB pulse width
maximum sidelobe for |t|<T
theoretical gating sidelobes = -20*log10(TB)-3 dB
maximum spurious for |t|>T
theoretical feedthru = CWFT-10*log10(TB)+6 dB
theoretical triple travel = CWTT -10*log10(TB)+3 dB
maximum s/n mismatch loss
if doppler is significant, then specify these parameters additionally at maximum doppler

6. Specify compressed pulse maximum widths at multiple levels only if truly necessary, and then only at ~10dB above the specified sidelobe level. The main pulse shape is not easily modified. Such specs can drive yields down and costs up. 7. Specify out of band rejection only if truly necessary. Define without tolerance the StopBands in which rejection levels are then specified. Do not extend the StopBands below Fo/2 or above 2Fo. 8. Test is performed in a 50 ohm system with return loss usually unspecified. If necessary, specify the minimum return loss either at F0 or in B. Return loss will always degrade near the PassBand edges. A 1dB increase in input and output return loss will cause a 1dB increase in insertion loss. Do not specify return loss outside the PassBand, assume it’s zero. 9. A polynomial is least mean squared fit to the un-wound measured phase(f), which is then displayed as the deviation from that polynomial. Midband delay (T0) is derived from the first order derivative of that polynomial at Fo, and chirp rate (S0 = T/B) from the second order derivative at Fo.
10. Dispersive filters are usually ovenized for temperature stability. If TCV is the temperature coefficient of SAW velocity, and dTemp is the temperature range/2, then dTemp must not exceed: for LFM dTemp < .2/(T*B*TCV), and for NLFM dTemp < .1/(T*Fo*TCV)
11. Specify the operating temperature range with care, an excess can drive yields down and costs up.
12. Non-operating temperature range can be -55C to 125C.