# Why don't people always use 50 ohm resistors when matching impedances?

Impedance matching when designing the RF receiver circuit and antenna design takes a lot of time and effort for VNA. People often use capacitors and inductors to match the impedance of the antenna transmission line. I want to ask why we don't use a 50 Ω resistor for impedance matching?

Using resistors in impedance matching saves me time and effort. What effect does it have on the performance of RF and antenna?

If I don't use resistors and only use inductors and capacitors, is there any way I can match the antenna's impedance faster?

• your third question is independent from your title and your first question. Please ask it in a separate question post! I'm removing it from your question here, but please don't take this personally – it's just to keep your title question focused, and the other question is very welcome (just: please ask separate questions in separate posts). Thank you! Mar 14 at 10:33

I want to ask why we don't use a 50 Ohm resistor for impedance matching?

Because

1. you can't get from any point to any point on the Smith chart using only one type of component; so, the proposal simply doesn't work
2. unlike L and C, R is actually a component that matches by converting energy to heat. That is usually the opposite of what you want; remember that you're matching to get the maximum amount of power from source to sink, not to convert it to heat!

If I don't use resistors and only use inductors and capacitors, is there any way I can match the antenna's impedance faster?

You honestly just need to practice with the Smith chart (I've been in the same situation as you, as have many here: I studied this just as you and finding matches took longer than I wanted to spend in the exam. I practiced!).

Generally, minimizing reflection through matching with components is just an optimization problem: If you need to do this fast, you'd let a computer do it, simply by writing down the formula of the reflection coefficient (that's the objective function that you need to minimize), depending on the values of the components in your matching network, as arises from network and four-port theory. Then you let an optimization algorithm find the optimum (under constraints, such as that the component values need to be positive, and within limits). For some simple matching network topologies, analytic solutions exist.

But if you're a human and you're understanding how to match something, there's few things as quick as being well-versed with a Smith chart!

I want to ask why we don't use a 50 Ω resistor for impedance matching?

Real resistors automatically consume power and reduce the signal by at least 6 dB. Using a tuned LC to match doesn't lose any power and, comes with the benefit of acting like a bandpass filter for the wanted signals.

Using resistors in impedance matching saves me time and effort. What effect does it have on the performance of RF and antenna?

There is a time and a place to use resistors for matching but, for most situations we don't want to lose signal power so we use LC circuits.

If I don't use resistors and only use inductors and capacitors, is there any way I can match the antenna's impedance faster?

Recognize that an antenna's complex impedance can be made resistive by the correct value conjugate impedance. Then, if the remaining impedance (resistive) doesn't match the transmission line, use a simple L-pad to match it (and avoid reflections and loss): -

I'd use a calculator (as per the above image) taken from my basic website. As you should be able to see, the voltage gain ($$\A_V\$$) to the output (in that example) is 2.44949 and, if you did that math, the power entering the L-pad from the left (at 50 Ω) is fully delivered to the load (at 300 Ω).

If you used a resistive L-pad to match impedances of 50 to 300 you'd get this: -

And notice that $$\A_V\$$ is only 0.52277. That's a power loss of 13.42 dB.

I'm sure that it's just acquisition of knowledge that's holding you back.