Drawing Spec Lines — "Out of Range" Is Not a Pass

Once a design is finished, how do you decide whether it is good enough? Rather than eyeballing numbers and going by feel, the reliable way is to draw the requirements as spec lines and judge mechanically.

There are only three kinds

Around matching networks there are really only three kinds of spec line:

All of them have the same form: "over a given frequency range, do not exceed / do not fall below a given dB value". Fix the range, the value and the direction, and you have drawn one spec line.

You need specs on both |S11| and |S21| because one of them alone is not enough. Watching return loss alone lets a circuit that turns power into heat pass.

Judging a real design

Take the circuit from the previous note: 200 Ω matched to 50 Ω, with the shunt C replaced by a trap that puts a notch at 2 GHz.

Set the specs as follows:

Spec 1  |S11| ≤ −15 dB   @ 0.9 to 1.1 GHz
Spec 2  |S21| ≥ −1  dB   @ 0.9 to 1.1 GHz
Spec 3  |S21| ≤ −30 dB   @ 1.8 to 2.2 GHz

The results:

It fails two out of three. Judged at the design frequency alone, the circuit is perfect: |Γ| is 1e−16 at 1 GHz, and the notch at 2 GHz is −240 dB on paper. It still does not meet the specs.

Why it failed

Both failures happen at the band edges.

Spec 1 fails at 1.1 GHz. The match is perfect at f0, but the bandwidth set by Q does not reach ±10 %.

Spec 3 is more extreme. The notch is infinitely deep at 2.0 GHz, yet −30 dB is actually met only over

1.932 to 2.081 GHz (149 MHz wide)

The spec asks for a 400 MHz wide stopband, so it falls far short.

This is what the previous note meant by "the deeper the notch, the sharper it is". The depth at the center and the width of the band are different quantities, and the spec asks about the latter. Taking the notch from −240 dB to −300 dB would not bring you one step closer to this spec.

The remedy is to gain width, not depth: split the resonator into two with staggered resonances, revisit the stopband requirement, and so on.

"Out of range" is not a pass

When implementing spec lines there is an unglamorous but important decision: how to treat a spec whose band lies outside the sweep range.

If you naively call it "a pass, because no point violated it", something dangerous happens. With the sweep narrowed to 0.9–1.1 GHz, the 1.8–2.2 GHz rejection spec is shown as "pass" without ever being judged.

The correct answer is "cannot judge". Neither pass nor fail — there is simply no data to judge it with.

Spec band not covered by the sweep  →  "cannot judge", not "pass"

This is the line a design tool has to draw so that it does not lie quietly. People relax when they see green, so nothing that has not been evaluated should be shown in green.

For the same reason, the habit from the two-stage note — widening the sweep to two or three times the design band — pays off. A narrow sweep will not tell you what it is not showing you.

How to draw spec lines

The order to follow when setting specs in practice:

1. Draw them from the requirements, not from the design result. A line drawn after looking at the design — "this much should pass" — is useless for judging
2. Include the band edges. The value at the center frequency plays no part in the verdict. Only the worst point matters
3. Build in margin. Fold part tolerance, temperature and assembly spread into the spec itself
4. Set stopbands from real interference sources. Not "2 GHz because it is the second harmonic", but work back from the transmitter's output spectrum or the regulatory limits

The first one above all. Draw the line after looking at the design and it will always pass. That is not judgment; it is rubber-stamping.

Try it

Spec lines are most effective when you can see them on top of the response.

Smith Match — Matching Network Designer

You can draw an upper limit on |S11|, and lower and upper limits on |S21|, each with its own band and dB value. There is no limit on how many, so when there are several stopbands, as in point 4 above, draw one rejection line for each. Pass and fail are shown by color, and a spec whose band is not covered by the sweep is treated as "cannot judge", not as a pass. The numeric readout is narrowed down to pass/fail for the same reason: whether the spec is met is the heart of the decision.