# Length-matching microwave differential traces

I'm driving an RF mixer that takes differential input signals. My max signal frequency is $$\6\,\text{GHz}\$$. I understand that the differential input signals need to be length-matched, but what sort of tolerance does this give me? In other words, how different can the lengths be? I'm asking because the mixer pin configuration makes it really tough to exactly match the lengths without doing some more funky stuff like adding serpentine traces. Moreover, based on my PCB stackup, each differential trace needs to be $$\0.85\,\text{mm}\$$ wide ($$\0.1524\,\text{mm}\$$ gap), which makes adding curves tricky without adding substantial length.

Here are my thoughts on the problem. The length matching in this context is important to minimize phase delay between the signals. Basically, we'd like the mixer to take the difference of the signal and its inverse, not the signal and a time-delayed copy of its inverse. The signal frequency components are sinusoidal and the value of $$\\sin(x)\$$ changes most quickly at $$\x=0\$$, where $$\\frac{d}{dx}\sin(x=0)=1\$$. So, if I wanted to keep the delayed amplitude within $$\1\%\$$ of the value it should be (for arbitrary phase), I should keep the length difference less than $$\1\%\$$ of the signal wavelength in the transmission line. In my case the electrical length is $$\30\,\text{mm}\$$ which means I should keep the length difference less than $$\0.3\,\text{mm}\$$. Is my logic sound? Is $$\1\%\$$ a sufficiently conservative value? Can I get away with more? Is there a rule of thumb for this? If the answer depends on information I haven't provided, please let me know and I'd be happy to include it.

So, if I wanted to keep the delayed amplitude within 1% of the value it should be (for arbitrary phase), I should keep the length difference less than 1% of the electrical length.

I'm not clear how you got to this rule, but I'd expect to have a rule that gives the length difference as a fraction of the signal wavelength (in the transmission line) rather than as a fraction of the trace length.

The reason is if you consider one of the two traces as "ideal", then you want to know how out of phase the signal on the other trace is at the receiving end of the trace, not at the source end.

That said, your trace length isn't that much different from one wavelength, so using a 1% rule will probably work well.

Can I get away with more?

Probably.

Depending on your requirements, the EMI (radiation) produced by common mode signals created by length mismatch might be a more important determiner of the maximum mismatch than your performance requirements.

• Apologies if my question was unclear, the length difference I computed is in terms of the signal wavelength in the transmission line. It looks like I may have misused the term electrical length. I meant wavelength in the tx line. Apr 15 '20 at 2:59
• @MattHusz, OK. FYI, the usual meaning of "electrical length" is the length of the transmission line expressed as a multiple of the signal wavelength. It is usually expressed in degrees or radians. (i.e. a $720^\circ$ electrical length is 2 wavelengths long). Apr 15 '20 at 3:02

consider the effect of mismatching ---- merely a phase-shift. why? because you are providing sinusoids.

As matthusz says, PI shaseshift results in no signal.

90 degrees causes 0.707 summation

60 degrees is 0.866 output.

Thus 10 or 20 degrees, compared to a radian (57.3 degrees) is less than a dB.

• A phase shift, plus it affects the amplitude, no? E.g. if I shift by $\pi$ I get no signal... So, takeaway is keep phase shift as small as possible? Any specific guidelines? Apr 15 '20 at 7:26