Back to Communication Products Group Technical Notes 25T014 Adjustment and Performance of Variable Equalizers
MITEQ TECHNICAL NOTE 25TO14 JUNE 1995 REV B ADJUSTMENT AND PERFORMANCE OF VARIABLE EQUALIZERS (SPECIFICATION SHEET D-107) The MITEQ Variable IF Group Delay Equalizer provides a means of compensa-tion for the non-linear delay and amplitude slope distortions that are introduced by the various components and subsystems of a satellite communications link. Group delay distortion can cause system performance degradation. These degredations are waveform distortions, intermodulation noise generation in analog FM systems, and intersymbol interference in digital systems. To compensate for these distortions, delay equalizers are used to generate a function which is opposite to that of the delay response of the unequalized system. Due to the nature of these distortions, it is necessary to have the capability of user adjustment. The MITEQ Variable IF Group Delay Equalizer is designed to allow all system group delay distortions to be eliminated by inserting compensation at IF frequencies (70 MHz or 140 MHz). A properly compensated group delay response will yield a constant propagation delay over frequency thereby eliminating any delay distortions. Figure 1. The Delay Performance of a Sample Filter.
Figure 1 shows the group delay performance of a fifth order elliptic function filter with a carrier size of 36 MHz at center frequency of 70 MHz. The rabbit ears occur at the approximate 3 db bandwidth points. To equalize this filter an oppposite delay response must be generated. To fully compensate the group delay over its entire passband is very difficult. Generally, only 80 percent of the filter s 3 db bandwidth need be compensated. All-pass Network An All-pass Network exhibits a flat amplitude response with respect to frequency but will introduce a phase shift versus frequency. This phase shift with respect to frequency is the group delay. If a network is to be of an all-pass type, the absolute magnitudes of the numerator and denominator of the transfer function must be related by a fixed constant at all frequencies so that the zeros of the network are the mirror images of the poles. Figure 2 illustrates the symmetrical pole-zero configuration in the complex frequency plane for the second-order all-pass transfer function. The transfer function of a second-order all-pass network is given by: (s 2 -ω r /Qs+ω r 2 ) T(s) = ------------------ (s 2 + ω r /Qs+ω r 2 ) The absolute magnitude of T(s) is unity, which is all-pass. The group delay is given by: 2Qω r (ω 2 +ω r 2 ) T gd = --------------------- Q 2 (ω 2 -ω r 2 ) 2 +ω 2 ω r 2 Where ω r is the pole resonant frequency and the pole Q =ω r /2a. Figure 2. Second-order All-pass Pole-zero Configuration. A standard bridge T-type Second-order All-pass Network is not suitable for use in tunable delay equalizers. The tuning of these sections makes it very difficult to meet group delay and amplitude response specifications simultaneously. If the inductors have insufficient Q, a notch will occur at the resonant frequency. Since this notch is unacceptable, adequate coil Q must be provided or amplitude-equalization be used. This additional circuitry further complicates the alignment. 2
A simpler, reflection type equalizer approach is used in the MITEQ Variable IF Group Delay Equalizer. This is shown in Figure 3. Transformer T loads a series resonant LC, and the balanced components R1, C1. The transformer provides isolation between the amplitude tuning elements R1, C1 and the frequency tuning elements L, C. The transfer function of this circuit is as follows: (s 2 -(2Z 0 s/l)+1/lc) T(s) = ----------------------- 2(s 2 +(2Z 0 s/l)+1/lc) The absolute magnitude of the transfer function is equal to a fixed constant at all frequencies. The resonant frequency is: ω r = 1/sqr(LC) and Q = ω r L/2Z 0 where Z 0 is the load impedance. Reflection Type All-pass Network. Figure 3. The group delay reaches a peak which occurs very close to ω r. As the Q is made larger, the peak delay increase and the delay response become sharper. The frequency of maximum delay is slightly below ω r. The delay at ω r is given by: T gd,max = 4Q/ω r = 2L/Z 0 ns L in nano Henries Changing the inductance value of L will affect the delay peak as well as the frequency of peak delay. 3
Single Section Delay Adjustment As stated previously, the peak delay is adjusted by varying the inductance L. As the peak delay is changed, the frequency of the delay peak also changes. The variable capacitor C is used to adjust the delay peak to the desired frequency. The peak delay is not changed when adjusting the peak frequency. The quality factor of the inductor Q 1 is not critical for this circuit, since the notch can be compensated by the resistor. Therefore, the tuning is simple. First, set the peak delay by adjusting the inductance, then adjust the capacitor to tune the peak frequency. Afterward, balance the amplitude response by trimming the resistor R1 and the capacitor C1. The effects of changing L and C on the delay peak are shown in Figure 4 and Figure 5. Figure 4. Delay Varying by Changing L. Adjust the capacitor C to return the delay peak to the center frequency). 4
Figure 5. Delay Varying by Changing C. The MITEQ Variable IF Group Delay Equalizer is designed to be used to equalize system group delay distortion in satellite communication earth terminals. The VEQ-2-70 operates in the 70 MHz ±18 MHz frequency range. The variable capacitor C can set the frequency of the delay peak from 52 to 88 MHz. The peak delay value, which is controlled by the inductor L, can be adjusted from 12 to 48 ns each section. A fine adjustment module is designed for peak delay from 3 to 12 ns. The VEQ-2-140 operates in the 140 MHz ±36 MHz frequency range. The frequency of the delay peak can be varied from 104 to 176 MHz and the peak value can be adjusted from 6 to 24 ns. When the inductor L and capacitor C are changed, the flatness of the amplitude frequency response change. It is necessary to adjust the balance components R1 and C1 to restore the flatness of the amplitude. The amplitude response varies by adjusting R1 and C1 are shown in Figure 6 and Figure 7 respectively. 5
Figure 6. Amplitude Varying by Adjusting R1. Adjusting R1 changes the amplitude response near the frequency of the peak delay. A peak or a notch on amplitude response will appear when the resistance is varied. It should be set to provide a flat amplitude response. The effect of adjusting C1 upon amplitude response is different from adjusting R1. The amplitude slope changes when the capacitance is varied. Due to the balance and slope adjust, the peak delay and center frequency will change slightly. Set the peak delay and the center frequency once again and trim the balance and the slope adjust until the amplitude response flatness is within ±0.1 db range. Figure 7. Amplitude Varying by Adjusting C1 6
Multiple Sections Delay Equalizer The group delay response of a single section equalizer is shown in Figure 4. The shape of the delay response looks like the frequency response of an LC resonant circuit. It is uniquely determined by the Q of the equalizer. Since the peak delay value, T g, dmax equals 4Q/w r, is made larger to compensate the system group delay, the delay response becomes sharper. The delay response of a single section is not parabolic over the entire frequency range. Only a small portion of frequency range near the peak is parabolic. But most of the system group delay will exhibit a response as a parabolic curve and tilt at its edge as shown in Figure 1. If a single section equalizer is used to compensate the system group delay, the combining group delay response will produce a large ripple. Cascading of two or more sections which are stagger-tuned to different center frequencies and have a different peak delay value, will provide a nearly perfect match to the desired equalization fit. For two or more sections in cascade, the composite group delay response is the sum of the individual group delay responses. No interaction will occur if there is sufficient isolation between each section. In actual circuits, attenuators and amplifiers are inserted between sections. An example of a three cascade section group delay response is shown in Figure 8. Figure 8. Example of a Cascade Three Sections Equalizer Delay Response. 7
Two equalizer delay sections are stagger-tuned about the center frequency, and the third section is tuned to the center frequency. The composite group delay response has a much wider parabolic bandwidth. As more sections are used, their frequency will be set further away from the center frequency, and usually their peak delay will be set larger. Multiple delay equalizer sections are needed to compensate the system group delay as shown in Figure 1. Several factors must be considered to acheive this end. How may sections are needed? What is the frequency of the delay peak for each section? What is the peak delay value for each section? The method for compensating system group delay developed by Richard P. Phillips (1980) may be useful. The method states that the number of delay equalizer sections depends on three factors: the number of poles in the filter, the desired delay flatness, and the 3 db bandwidth of the delay response. One equalizer section will generally be needed for each filter pole to achieve total flatness over its entire passband. As the allowable delay variation increases, and the equalized portion of the 3 db bandwidth decreases, fewer sections will be required. Mr. Phillips procedure is based on measured delay data plotting on a graph that contains several selected curves for delay equalization networks for one to eight equalizer sections. Mapping begins by selecting a trial variable T te and plotting the delay data on the chosen normalized delay equalizer curves. The value T te is then increased or decreased. Once a suitable match has been found between the filter delay data and one of the equalizer curves, design parameters (namely, the peak delay and its frequency) can be determined. A computer-aided realization program was developed by Robert C. Kane (1989). The development leads to a software routine which performs the iteration over a specified range of parameters and searches for the most appropriate equalizer. A modified version of the CAD program was written and used by a MITEQ engineer to help a customer solve his group delay equalization problem. For most VEQ delay equalizers users, the equipment is used for field adjustment. A computer is not available for the purpose of alignment. The field engineer or technician must use traditional trial-and-error methods. There is no standard procedure to make the alignment. The next section will describe an alignment procedure to compensate the group delay of a sample elliptic function filter. The response is shown in Figure 1. Multiple group delay equalization sections are always needed to obtain the desired delay response. The MITEQ Variable IF Group Delay Equalizer VEQ Series provides two to twelve delay sections per channel. Each section has a bypass switch to switch the section in or out of the signal path. A fine tuned delay module is also available for the user s option when fine tuning is needed. 8
Alignment to a Specific Group Delay Repsonse The equalization of group delay starts at the measurement of the delay data. It can be the group delay of a satellite transponder or a bandpass filter, etc. The group delay response shown in Figure 1 will be used as an example to demonstrate the procedure of alignment. It is recommended that the alignment procedure below be used first. Intuition and experimentation with different procedures will enable the technician to find the procedure that works best. The number of sections used will depend on the amount of equalization required. Due to the fact that there are four adjustments per section, it is recommended that the fewest number of sections be used. This will ease alignment. 1. Measure the satellite transponder group delay characteristic to be equalized. Draw the inversed group delay characteristic to be equalized. Draw the inversed group delay curve on a transparent paper with the same grid scale of the measurement instrument as shown in Figure 9. Attach it to the screen of the instrument. The delay contains a mixture of linear and parabolic delay characteristics. The Variable IF Equalizer should be tuned to the inverse of the transponder group delay characteristic. Figure 9. The Inverse Group Delay Response of the Sample Filter. 2. Switch a section out of BYPASS mode. 3. Use the DELAY ADJ to set the amount of delay appropriate to equalize the group delay response. 9
4. Use the FREQ ADJ to set the peak frequency of the group delay response. Compensate for linear delay by setting the peak frequency below or above the center frequency. 5. Use the BAL ADJ and SLOPE ADJ to flatten the amplitude response. 6. Most equalization requirements require a cascading of two or more sections to match the desired equalization. Using two sections of the same peak delay value with a frequency offset, and equal amounts above and below the center frequency, can provide a much improved equalization fit. Switch another section out of BYPASS mode. Repeat Steps 3-5. 7. Repeat for as many sections as necessary. There wil be interaction between sections. The peak frequencies of adjacent sections should be staggered as far as possible to minimize the interaction. These adjustments must be retuned. The composite six sections and each individual group delay response are shown in Figure 10. The delay response is a near perfect match when the inverse group delay characteristic curve of the sample filter is within the 3 db bandwidth. Figure 10. Group Delay of Six Section Equalizers.
8. Once the Variable IF Equalizer has been initially aligned to a required group delay response it can be integrated to the transponder system. Final adjustment is required for reduction of the delay ripple by reducing or increasing the peak frequency or peak delay value of each equalizer section which is centered near the frequency of the delay ripple. Repeat Step 5 for each section to set the amplitude response for maximum flatness. Figure 11. The Equalized Group Delay and Amplitude Performance of the Sample Filter. The equalized group delay and amplitude response of the sample filter is shown in Figure 11. Prior to equalization, the group delay variation is 50 ns over 52 to 88 MHz frequency range. After equalization, the overall delay variation falls within 2 ns and the amplitude response remains flat within ±0.1 db. In some cases, where the delay curve has a steep delay near the band edges and corresponding large delay variations, using two or more simple, multisection equalizers to replace one complex equalizer may be considered. The delay curve is split to several shallow delay curves with less delay variation. Each of the shallow delay curves can be equalized more easily than the original curve, and the resulting equalizer is often easier to align (Phillips, 1980). The MITEQ Variable IF Group Delay Equalizer VEQ Series also provides amplitude slope adjustment through a front panel slope adjustment potentiometer. The amplitude slope adjustment range is ±3 db. The gain of the VEQ Equalizer is 0 db. An option of 10 or 20 db gain version is available. References Phillip, Richard P., "Curve-Matching Method Specs Delay Equalizer" in Microwaves, pp 67-78 11
(September 1980) and pp 65-71 (October 1980). Kane, Robert C. "Bridge-Tee Delay Equalizers - A Computer-Aided Realization" in RF Design, pp 63-68 (April 1989) M:\TECHNOTE\25T014.DOC 12