Theory vs Practical - Amplifier matching networks - Page 1
Forum section: electronics / rf-microwave

author: fourierpwn
author_rank: Regular Contributor
timestamp: June 13, 2019, 01:05:07 am
content: I am trying to learn the art of amplifier design (mainly PAs, but have interest in LNAs too). While I'm still trying to wrap my head around running load pull simulations to find optimal impedance/gamma points etc. I have noticed that all of the theory and examples make use of simple 1,2 or 3 stub tuning networks (planar based designs for RF), then when you see industry and research based designs it seems like the matching networks are a lot more complicated than just these (at most) 3 stub networks. Why is this so?My initial guess is that in practice you need to consider the harmonics and also tune these too so then the matching networks grow in complexity. Though, this is merely a guess and I would like to know for sure. I'm sure some examples would help but I'm travelling at the moment and don't have anything on-hand sorry. Can post some later if needed.

author: RoGeorge
author_rank: Super Contributor
timestamp: June 15, 2019, 04:42:56 pm
content: 1. An impedance match is valid only at the design frequency.2. The bigger the difference between the source impedance and the load impedance, the narrower the bandwidth where the matching stays good enough.When there is a big step in impedance, the resulting bandwidth might be too small to be usable, but there is a trick. The trick is to match the impedance in smaller steps, thus chaining more then one matching cell between the source and the load.More steps in impedance between the source and the load will flatten the frequency response, but will complicate the matching network.I guess this is what you were asking about, because without schematics and examples it can be anything.

author: rf-messkopf
author_rank: Regular Contributor
timestamp: June 19, 2019, 03:06:44 am
content: You did not say if you are interested in matching at a single frequency or over an extended frequency band.As has already been pointed out, the complexity of the matching network is often about bandwidth, and also about its physical realizability at a particular frequency. In fact, an arbitrary impedance (with non-negative real part) can always be matched at a single frequency to any characteristic impedance of a transmission line with only two lumped reactive elements. Similarly, a single stub can match an arbitrary impedance (with non-negative real part) at one frequency to the characteristic impedance of a transmission line, provided both the stub length and its distance from the load can be varied.There are a number of theoretical results which lead to more complex matching networks. For example, it can be shown that an impedance which varies arbitrarily with frequency can be approximately matched over an arbitrary frequency band using networks consisting of \$N\$ line sections of different characteristic impedance (the so-called multi-section transformer), where \$N\$ grows with the precision of the match. (This becomes quickly impractical for large \$N\$, so that one uses certain tapered lines to achieve an approximate match, for example the Klopfenstein taper.)Of related interest is the Bode-Fano theorem, which provides a limit to the precision with which certain certain networks can be matched to a given characteristic impedance. For example, if a parallel circuit of a resistor \$R\$ and a capacitor \$C\$ is to be matched by a lossless matching network, then for the reflection coefficient \$\Gamma(\omega)\$ looking into the network the inequality\[\int_0^\infty\ln\Bigl(\frac{1}{\lvert\Gamma(\omega)\rvert}\Bigr)\,\mathord{\rm d}\omega\leq\frac{\pi}{RC}\]holds. I.e., there is a limit to the "smallness" of \$\lvert\Gamma(\omega)\rvert\$ over an extended frequency interval. And in particular, the reflection coefficient cannot be zero over a frequency interval with nonvanishing length.Edit:Essentially, this is a more mathematical version of what RoGeorge has said in plain words.

author: TheUnnamedNewbie
author_rank: Super Contributor
timestamp: June 19, 2019, 04:32:43 am
content: Are you looking at integrated circuits, or discrete components?Quote from: fourierpwn on June 13, 2019, 01:05:07 amCan you show some examples of these 'a lot more complicated networks'?With integrated circuits, transformers (like, actual transformers with two coils) can be used too, though this mainly becomes practical at high frequencies (high being above a few tens of GHz). My main experience is with circuits at those very high frequencies, and there, usually, the bandwidth provided by a simple match is sufficient for what you want to do (Keep in mind, a few percent relative bandwidth at 140 GHz is already an absolute bandwidth of many GHz).I think lumped-component matching is also common at lower frequencies in integrated circuits, as the sizes allow you to think of stuff in a lumped-element way, even if you are operating at say 5 GHz or even higher.

author: tdhodge
author_rank: Newbie
timestamp: June 25, 2019, 04:28:57 pm
content: Quote from: fourierpwn on June 13, 2019, 01:05:07 amYou're right about the harmonic tuning. Look up harmonic matching network or harmonic impedance matching. For switching amplifiers, turns out to get higher efficiencies you need to be able to control higher harmonics. A classic example is a class F or F^-1 amplifier. Ideally the voltage waveform across the transistor doesn't overlap with the drain current waveform during a conduction cycle so zero power is dissipated.In practice, the drain capacitance will short out higher harmonics of a device so most designs control up to the 3rd or 5th harmonic. You will also be limited by the transition frequency of the device you are using.