In RF circuits, circuits are often required to match 50 ohm to another impedance (75 ohm for example). In this post we provide two different types of matching circuits with calculators
- Resistive
- Reactive
We also explain the pros and cons of each
Resistive Match
The resistive L-network below is used to match two resistive impedance values. The parallel resistor Rp goes across the smaller impedance R1 and the series resistor is placed between the input and output. The configuration is also called a Minimum Loss Pad.
Use the calculator below to calculate Rs and Rp. Note that the value of R1 should be less than R2.
Resistive Match Calculator
Example calculation – 50 ohm to 75 ohm matching
Use the calculator above with R1 = 50 Ω and R2 = 75 Ω. The values of Rp = 86.6 Ω and Rs = 43.3 Ω can be used to match 50 to 75 ohm with a resistive L network.
One of the biggest advantages of this type of network is that it represents a broadband match that does not depend on frequency.
The circuit is lossy and the calculator also provides the value of attenuation – in this case 5.7 dB. That’s a significant reduction in power by a factor of 73% (use the dB to linear calculator to see that Pout/Pin = 0.27)
This naturally leads to the question: What if 50 ohm were not matched to 75 ohm?
The answer can be found by using the impedance mismatch loss calculator. The mismatch loss is calculated to be 0.18 dB. As a result of this mismatch, only 4% of the incident power is reflected back, while 96% is transmitted forward. Not a big deal in most situations and the resistive match by comparison produces a poorer outcome.
Example calculation – 50 ohm to 300 ohm matching
The folded dipole has an impedance of 292 ohm. 300 ohm balanced transmission lines, such as twin-feed ribbon cable can be used to feed such antennas. What if the impedance of the transmission line is 50 ohm? In that case, ground one of the terminals and use the calculator to find:
- Rs = 274 Ω
- Rp = 55 Ω
You can pick resistors close enough to these values
The total loss in this case is -13.4 dB. The resistors provide a broadband match.
In the case of a dipole antenna that’s designed for a narrow range of frequencies, matching over a large range is not necessary and can be a negative.
What is the alternative?
A good alternative is a lossless matching network. Let’s take a look at this configuration next.
Reactive Matching Network
A reactive matching network with parallel Inductor and Series Capacitor is shown in the picture below.
Unlike the resistive match, this L network is lossless.
The only disadvantage of the reactive matching network over the resistive one is that resulting match is perfect only at a single frequency. It is “good enough” over some range of frequencies around it.
Use the calculator below to compute values of Lp and Cs.
Reactive Match Calculator
Example calculation – 50 ohm to 75 ohm matching
Use the calculator above with R1 = 50 ohm and R2 = 10,000 ohm. The values of Lp = 11.28 uH and Cs = 22.57 pF can be used to match the two impedances.
For this calculation we used the Quality factor
Q = √((R2/R1) – 1) where R2 > R1
As the ratio of the impedances increases, Q increases. This reduces the bandwidth over which the match is good.
Summary
In this post we presented two types of L matching networks – Resistive and Reactive. The resistor configuration presents a lossy, broadband match while the reactive configuration (consisting of an inductor and a capacitor) presents a lossless, narrowband match. A reactive match makes more sense over a smaller range of frequencies, as is the case with antennas.
References
[1] Equations for the matching networks are presented in The Art of Electronics by Horowitz and Hill
Related Calculators
- S11 to Impedance – find the impedance value for a certain value of reflection coefficient