Matching Pads

Suppose you are connecting a 75-Ω cable to a piece of 50-Ω test equipment, or perhaps you are hooking up a pc-board trace to an unusual cable. If the transmission lines on either side of the connecting junction are long (compared with the signal rise or fall time) and if the shift in impedance is significant, reflections from the junction may degrade your signal. To fix the degradation problem, you can add circuitry at the junction.

The objectives for junction-matching circuitry vary according to your needs. Sometimes you want to cleanly pass signals in just one direction, the other direction, or both. Whatever the direction of signal flow, you want the signals to traverse the junction with minimal distortion, attenuation, and reflections. You can configure the circuit in Figure 1, called a resistive matching pad, to accomplish all of these objectives.

Figure 1 -- A resistive pad matches two circuits with characteristic impedances Z1 and Z2 (Courtesy of EDN)

In ac-coupled applications, in which no meaningful dc content exists, you can use a transformer to modify the circuit impedance. Examples of wideband applications with no meaningful C content include audio, video, and some data signals specially coded to enforce an equal number of ones and zeros (such as Manchester data coding or 8B10B coding). The transformer is a good component to use for impedance translation, because by winding different numbers of turns on the primary and secondary of the core, you can amplify (or attenuate) the voltage at the expense of an opposite change in current. Unfortunately, transformers don't work at dc.

In narrowband applications, such as carrier-based AM or FM radio, you can sometimes use resonant-circuit tricks to accomplish impedance transformation. A classic example is the resonant pi filter. It can accomplish signal amplification (or attenuation) over a narrow band of frequencies but not over a wide band.

Random digital data, whose spectrum spreads across a vast range from dc to daylight, renders useless all standard narrowband and ac-coupling tricks. The only passive circuits that guarantee good impedance translation for wideband signals are resistive pads.

You can configure the matching pad shown in Figure 1 in four ways. Table 1 presents the required component values for each application. The "optimized" designs minimize the reflection coefficient in the prescribed direction at the expense of some loss in overall transmission gain. The directions are oriented as shown in Figure 1, going from left to right (L—>R), or the other way (L<—R). The "both ways" minimizes the reflection coefficient in both directions and in doing so suffers the greatest transmission loss.

Table 1-Matching pad design

Condition R1 R2
Unmatched 0
Optimized L—>R Z1Z2/(Z2Z1) 0
Optimized L<—R Z2Z1
Both ways Z1/K Z2K

Each row of Table 2 shows the performance of the four designs. The signal gain G (never bigger than unity) and reflection coefficient Γ (bounded by ±1) are then given for signals traveling in either direction. Without loss of generality, the table assumes that Z1<Z2. (If your circuit is the other way around, then you need a mirror-image version of Figure 1.)

When you configure the circuit for optimal operation in one direction, and send signals through it in the other direction, the reflection coefficient is not very good. In fact, it's worse than with a raw, unmatched junction. Sometimes such lopsided performance is acceptable. For example, using a good source-terminated network (source on the left), when the driver emits a fresh edge, you don't really care what bounces off the matching pad in the L—>R directions. Whatever bounces merely returns to the source termination and dies. You do, however, care about the signals that reach the end and then bounce off the massive open-circuited endpoint at the far end of the line. These signals, on their return trip, take a second pass across the matching pad (this time going L<—R), so the reflection coefficient to left from right mostly determines the performance of the system in that case.

For an application with Z1<Z2 using a source terminator, choose the optimized L<—R configuration. For an end-terminated driver on the same line, the optimized L—>R configuration works best. The both-ends termination (using both source and end-termination) is the least sensitive of all configurations to reflections at the junction. With both ends terminated, your circuit may not need a matching network at all.

For an application with Z1>Z2 using a source terminator, you must flip Figure 1 around backwards. That reverses the orientation of right and left, flipping the shunt resistor away from the driver onto the far side of R2. In this case for a source-terminated line you should choose the optimized L—>R configuration from Table 1. For an end-terminated driver on the same line, use the optimized L<—R configuration. The both-ends termination (using both source and end-termination) is the least sensitive of all configurations to reflections at the junction. With both ends terminated, your circuit may not need a matching network at all.

If you have any doubts about the direction, use Spice.

In all cases the variable K is defined as:

K=(1 – Z1/Z2)1/2

Table 2-Matching pad performance

Condition L—>R
Unmatched 2Z2/(Z2+Z1) (Z2Z1)/(Z2+Z1) 2Z1/(Z2+Z1) 2(Z2Z1)/(Z2+Z1)
Left-to-right optimized 1.000 0 Z1/Z2 –(Z2Z1)/Z2
Right-to-left optimized 1.000 (Z2Z1)/Z2 Z1/Z2 0
Both ways 1/(1+K) 0 1–K 0

To match two differential circuits with differential impedances Z1 and Z2, respectively, place R1 directly between the two conductors of impedance Z1. Then split R2 into two resistors, each of value R2/2. One the upstream side of R1 (the Z1 side), place these new resistors in series with each of the signal conductors.