Impedance matching on RF PCB

I have two questions about a power amplifier board, see picture.

1. The output of the amplifier has irregular copper traces with different lengths to the output SMA, which I marked (1). Doesn't this affect the impedance of the trace?

2. What is the use of two vertical traces before the output SMA, which I marked (2)?

This is an approximate equivalent circuit.

I have also drawn dotted lines to demarcate the boundaries between certain regions.

The basic method is to use transmission line sections as impedance transformers and lowpass filters.

In a given band, there exists an equivalence between an LC lumped equivalent circuit (for which we have standardized filter tables), and a network of transmission line elements, typically λ/4 segments (or multiples thereof), but shorter and longer elements are also used when some reactance is desired.

The characteristics of a transmission line segments are its electrical length (the time delay between its ends) and characteristic impedance (here, corresponds to trace width, wider = lower Z). These correspond to the L and C equivalents as $$\F_0 = \frac{1}{2 \pi \sqrt{LC}} \propto \frac{1}{t_0}\$$ and $$\Z_0 = \sqrt{\frac{L}{C}}\$$.

The transistor drain connects to a very wide pour, in fact it's about as wide as the λ/4 segments are long, which can be tricky for reasons of having resonant modes within that pour itself*, but mainly due to its wide aspect it acts like a capacitor, which I have labeled C1. This is resonated against the inductance of the "1" trace, which is quite wide, but less so compared to C1. This sets up a series resonant circuit between C1 and C2. Where is C2? C2 is the distributed capacitance of the "1" trace: a transmission line can be described as a continuous distribution of differential (very small bits of) L and C pieces. Mostly, the left half of the L's add in series, and the right half of the C's add in parallel, but there's some contribution from each bit of L and C all along the trace.

Actually, the "1" segment may be more like 5/8 λ, but there may also be some effect on velocity factor because this trace has more fields within the board than in the space above it (thinner microstrip traces have a significant contribution to their impedance from fields in the air), so perhaps the fields are -- well, they'd be slower if anything, really, making it even longer (electrically) than it looks.

*That is, it acts less like a (one-dimensional) transmission line and more like a (two-dimensional) cavity, with various resonant modes bouncing around within it. Presumably, this consideration has either been made as part of the design, or the filtering present here (or the transistor's own frequency response) is adequate to control for that (i.e. it's not a problem if such frequencies either are never generated in the first place, or aren't transmitted to the output port).

A more simplified interpretation of the "1" segment is as a λ/4 impedance transformer. When you have some impedance Z connected at one end of a quarter wave transmission line, the reciprocal of that impedance appears at the other end -- the reciprocal that is with respect to the line's own [characteristic] impedance. So, $$\Z_2 = \frac{{Z_0}^2}{Z_1}\$$. The transistor has quite a low impedance, 1-2 ohms (due to the high current of its operating range: approx. 28V / 20A), so to match up to 50 ohms or so, a transformer with intermediate impedance is required (maybe 7-10 ohms), which will therefore have an impedance around 1-2 ohms at one end, and 50 at the other.

Datasheet for reference: BLF2425M9LS140 Notice the impedance (conveniently given as ohms, not in terms of scattering parameters actually) given in §7.2.

C11 is a coupling capacitor to remove DC from the output. Its value is probably large enough to be ignored (i.e., a few ohms reactance), but may still be used as a highpass filter element. The length of trace it's on may be relevant; it's probably close to 50 ohms, so may be fairly neutral in effect, or perhaps it's a bit lower impedance, and has some relevant shunt impedance.

By the way, "shunt" means "connected from line to GND", and "series" means inline. So L2, C11, etc. are in series, and C1, C2, etc. are in shunt. This equivalent diagram is a ladder type network, which always has alternating series and shunt elements (or groups thereof).

The "2" section is a lowpass filter. The trace width is thinner here, suggesting higher impedance; whether this is higher than 50 ohms, or just relative to the surroundings, isn't evident. Again, λ/4 segments are used, here with stubs (the spokes to nowhere) which act as series-resonant "traps", shunting the signal path at resonance; and the series (L6-C4) link between them which acts to transform their impedance (making this a 2nd order filter).

Note that the two spokes act in parallel, being the same length and therefore L and C equivalents. They are independent, but because they respond identically (or as near matched as they are; they look pretty close anyway), they're effectively one thicker stub.

There are also bias tees, L1 and L3, also probably λ/4 stubs, to supply bias voltage to the gate, and DC power to the drain. Since one side is shorted (at AC, by a stack of bypass capacitors in parallel), by the λ/4 impedance transformer theorem, they are effectively open-circuit at the signal end. So they have essentially no impact on the signal along the main path, while still being able to supply DC to these nodes.

Disclaimers:

I haven't actually designed such a circuit before. I know the broad strokes how to do it, I just lack the tools (I don't have ADS or similar network design or field simulation tools). As a qualitative explanation was desired, this seems adequate.

Without PCB specs, a detailed analysis isn't possible, anyway; and it seems likely given the nature of the question, that a precise (quantitative) analysis wouldn't be fruitful anyway.

I will note the design is probably centered on 2.4GHz (ISM band), given that's what the transistor is intended for, and the approximate length scale of the photo.

• I am consistently amazed by the quality of the answers on here. Commented May 8, 2023 at 21:13

Both of those structure are to impedance transform and match the output of the amplifier to the load, that's connected to the SMA connector.

The two vertical traces are tuning stubs. There are lots of resources on how they work and how to design with then on the internet.