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Kalaiselvan Raghavan and Giridharan Krishnamurthy, Mini-Circuits
Impedance matching is a complex subject cloaked in a certain degree of mystery. Whenever a circuit fails or systemic problems are encountered, impedance matching is most often attributed as the cause. As a result, there are many situations in which it becomes necessary to match the impedance of a load to that of the source in order to maximize power transfer. There are many different techniques for impedance matching, and the best application of each will depend on the situation. This article will review the basics of impedance matching and describe some of the effective techniques commonly used to overcome impedance mismatch in a circuit.
The primary figures of interest in evaluating impedance mismatch are the voltage standing wave ratio (VSWR), return loss, and mismatch loss. These are defined below for review:
When a transmission line is terminated with impedance, ZL that is not equal to the characteristic impedance of the transmission line, ZO, not all of the incident power is absorbed by the termination. Some of the power is reflected back to the source so that phase addition and subtraction of the incident waves creates a voltage standing wave pattern on the transmission line. The ratio of the maximum to minimum voltage where the successive maxima and minima are spaced by 180˚ (λ/2) is known as the voltage standing wave ratio (VSWR).
Return loss is a measure in dB of the ratio of power in the incident wave to that in the reflected wave. Return loss, by this definition, always has a positive value. For example if a load has a return loss of 10 dB, then 1/10 of the incident power is reflected. The higher the return loss, the less power is lost from the thru-signal.
This is a measure of how much the transmitted power is attenuated due to signal reflection. Mismatch loss is determined by the following equation:
Where is the reflection coefficient.
For example, a filter with VSWR of 2:1 would have a reflection coefficient of 0.333, a mismatch loss of 0.51 dB, and a return loss of 9.54 dB (11% of the transmitted power is reflected back). In some systems, this is significant and indicates the need for components with low VSWR.
Impedance mismatch in a circuit can be caused by a number of factors. These include discontinuities in the physical path of transmission which reduce the quality of the signal; improperly terminated lines; and sudden step discontinuities in impedance lines. Of these causes, impedance lines with sudden step discontinuities are most common because customers often use substrate materials with different trace widths than those recommended by the component manufacturer.
Consider the suggested land pattern in figure 1 showing the footprint of a band pass filter. The green pads denote the signal pad, and the brown pads denote the ground pads.
In general, if the RF trace matches the width of the signal pad exactly, then signal reflection is minimized. The simulated return loss response for the three cases drawn in figure 1 is shown in figure 2.
Case 1 has a signal pad to transmission pad width ratio of 1:4 and return loss of 5 to 10 dB; case 2 has a ratio of 1:1.6 and return loss from 10 to 15 dB; and case 3 has a ratio of 1:1 and a return loss of >30 dB across the swept frequency range. This demonstrates that the impedance mismatch is inversely proportional to the ratio of signal pad width to transmission pad width. Mismatch is minimized when the signal pad and transmission pad are the same width.
There are multiple techniques that can be applied to improve matching in a circuit. One such technique is to insert a matched attenuator in front of a mismatched load impedance. The mismatch observed at the input of the attenuator is improved by an amount equal to twice the value of the attenuator. For example, consider a 3 dB attenuator. The signal at the input of the attenuator will experience a 3 dB reduction in power by the time it reaches the load. That signal will be 100% reflected by the load and experience another 3 dB reduction in power before returning to the input for a total reduction of 6 dB. Hence the return loss improves by 6 dB, thereby improving the match. The disadvantage of this technique is that the amplitude of the thru-signal is also reduced by 3 dB, which must be compensated for in adjacent networks.
An LC network can also be used as a matching network. This is basically an L-network, which is a simple inductor-capacitor (LC) circuit that can be used to match a wide range of impedances in RF circuits. There are four basic versions of the L-network with two low pass versions and two high pass versions. The low pass versions are probably the most widely used because they attenuate harmonics, noise, and other undesired signals, which is usually necessary in RF system designs. While the L-network is very versatile, it may not fit every situation. There are limits to the range of impedances it can match. In some instances, the calculated values of inductance or capacitance may be too large or small to be practical for a given frequency range. This problem can sometimes be overcome by switching from a low pass L-network to a high pass L-network or vice versa.
Another popular technique is using impedance matching transformers. These transform the load impedance as a square of the voltage-transformation ratio. The ratio of the voltage transformation depends on the number of turns on the input winding (primary), divided by the number of turns on the output winding (secondary). For radio frequency use, transformers are sometimes made from configurations of transmission line, sometimes bifilar or coaxial cable, wound around ferrite cores. This style of transformer provides extremely wide bandwidth, but only a limited number of ratios (such as 1:9, 1:4 or 1:2) can be achieved with this technique. At the same time, the ferrite increases the inductance dramatically while also lowering its Q-factor. The cores of such transformers generally enhance performance at the lower end of the frequency range.
Mini-Circuits CBP-1300F-1+ is a ceramic resonator band pass filter with a pass band from 1200 to 1400 MHz. A particular customer had used this model on a PCB such that the ratio of signal pad width to transmission pad width was 1:4. The customer sought recommendations to improve the matching of the circuit, and Mini-Circuits offered two suggested options.
As we’ve shown, modifying the width of the signal pad to match the width of the transmission pad will minimize mismatch between the component and the substrate. The customer board layout and the suggested modification are shown in figure 3.
The modified layout was tested in comparison to the customer’s board layout by sweeping return loss measurements from 1000 to 1700 MHz. Results from the test are shown in figure 4.
Testing revealed that altering the signal pad width significantly improved matching. The solid red trace in figure 4 shows the return loss performance of the customer’s board layout of about 10 dB. The dotted green trace shows the return loss performance after the signal pad width was modified. Return loss in this case improved to about 20 dB and pass band ripple has been significantly reduced as well.
Another method to improve matching in the circuit is to connect an 18nH inductor to ground at the output of the filter as shown in figure 5. This creates an LC matching network where the shunt capacitor effect is reduced by resonating with the 18nH inductor.
Again, testing was performed comparing the return loss of the customer’s board layout to that of the alternate layout across the 1000 to 1700 MHz range. Results are shown in figure 6.
Connecting an 18nH inductor to ground has again improved matching in the circuit. The solid red trace represents the return loss performance in the customer board which has return loss of about 10 dB and the dotted blue trace shows the performance after connecting a 18nH inductor to ground at the outout. Return loss in the latter case was improved to 20 dB and passband ripple has been reduced.
Impedance matching is a problem that arises in many circuits, and techniques to improve mismatch are often necessary. The solutions discussed above can help provide good impedance matching when a customer’s circuit board has different pad layouts than those of the component being used. The most appropriate technique will depend on the particular circuit and cause of the mismatch.