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I think by now I get complex impedance, the Smith chart, and antenna matching, but I am wondering how in an RF transceiver, i.e. a radio, the amplifiers on the transmitting and the receiving end are also matched to the impedance?

For the receiving side, I can imagine a few ways for the transmission line after the antenna to see e.g. 50 ohms towards the receiver (assuming the antenna and transmission line are already 50 ohms, or we a past a matching circuit), but none are very satisfying:

  1. The amplifier's input impedance is somehow 50 ohms. If so, how does that work in practice? Usually a common collector amplifier's impedance, for example, is much higher?
  2. The transmission line is merely terminated in 50 ohms, with a regular 50 ohm resistor, and the amplifier just samples the signal with a much higher input impedance. But is that really effective given that we want to amplify very weak signals? Would we not want the amplifier itself to be matched to transfer all the power to it?
  3. The input impedance of the amplifier is a higher but known value, and there is another matching circuit in front of the amplifier circuit. If so, is varying beta a problem, or is that negligible?

And what about the transmitting side?

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2 Answers 2

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  1. The amplifier's input impedance is somehow 50 ohms. If so, how does that work in practice?

In a receiver, the front-end amplifying device is more likely to be common-emitter or common-base rather than common-collector. But all three configurations can have power gain.
Common-emitter amplifier might just naturally have an input impedance near 50 ohms if it is biased with high DC current.

Shunt feedback is another way to lower input impedance of a common-emitter amplifier. Gain is lowered as well. Other benefits: wider bandwidth, less distortion, less likely to oscillate:

schematic

simulate this circuit – Schematic created using CircuitLab

  1. The transmission line is merely terminated in 50 ohms, with a regular 50 ohm resistor, and the amplifier just samples the signal with a much higher input impedance. But is that really effective given that we want to amplify very weak signals? Would we not want the amplifier itself to be matched to transfer all the power to it?

Not a good plan, if you want a low-noise amplifier. The regular 50-ohm resistor does terminate the transmission line, but dissipates away at least half the signal power, robbing the following amplifier. Your last statement is correct - maximum power is delivered to an amplifier whose impedance matches the transmission line.

  1. The input impedance of the amplifier is a higher but known value, and there is another matching circuit in front of the amplifier circuit. If so, is varying beta a problem, or is that negligible?

This is a common scenario in narrow-bandwidth amplifiers.
For a receiver, you want to knock down all signals whose frequency differs from the desired frequency before amplification. So a narrow-bandwidth filter is often placed between antenna and front-end amplifier. Most filters can be easily adapted to transform impedances losslessly.
Transistor gain can be a problem here, especially if amplifier output impedance is high as well as amplifier input impedance...oscillations can rear their ugly head.

TimWescott makes the point that noise match might trump impedance match in importance for a front-end amplifier. Another important consideration is linearity. You don't want that front-end amplifier generating spurious signals.
Front-end amplifiers might have gain reduced with negative feedback to allow larger input signals before distortion causes spurii...every amplifier distorts if you apply a large-enough input signal.
It is difficult to make a linear amplifier that also pulls low DC current from its bias supply.


Impedance in transmitters deserves a separate question, if not a whole book.

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First, with feedback and particularly in narrow band, you can fairly easily change the input impedance of an amplifier.

Second, for a receiver, you often don't care about getting a good impedance match to the antenna. However, you do care about presenting the optimal impedance to the receiver's front end, and this impedance is often not equal to the amplifier's input impedance. Google "noise match" for more detail. So, basically, it's pretty common that a receiver's LNA (the first amplifier in the chain) doesn't have a power match to the incoming transmission line.

Third -- and I don't know how often this is used, but I'm pretty sure it's not very often -- there are methods of applying feedback with lossless components (i.e. resonators and/or transformers) that allow you to both get a desired impedance and a noise match to a transmission line. Hayward's "Introduction to RF Frequency Design" has a description of this, somewhere (Wes Hayward designed spectrum analyzers for Tektronics, where it does matter that you have both an impedance and a noise match).

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  • \$\begingroup\$ Thanks, but why do we often not care about a good match between antenna and amplifier? With those tiny signals, don't we want as much power as possible ending up in the amplifier? \$\endgroup\$
    – anyfoo
    Jun 27, 2022 at 21:26
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    \$\begingroup\$ @anyfoo For weak signals you want the best signal to noise ratio (SNR) possible. If tuning for best noise match gives a better SNR than tuning for best power match then you tune for best noise match. \$\endgroup\$
    – Graham Nye
    Jun 27, 2022 at 21:39
  • \$\begingroup\$ I see. So what mechanism do, say, ham radio receivers use to define the impedance of the amplifier then? If I look at some ham radio schematics after a quick Google search, I have trouble identifying what defines the impedance of the amplifier in general. Like in this one, for example: homemade-circuits.com/… \$\endgroup\$
    – anyfoo
    Jun 27, 2022 at 21:51
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    \$\begingroup\$ Often they don't. When they do, it's either by using feedback, or with impedance matching networks, or both. \$\endgroup\$
    – TimWescott
    Jun 28, 2022 at 2:13

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