HB simulation with multiple square-wave signal

The purpose of the initial transient is to assist with convergence. As a result, only a single tone (the first tone) is enabled in the initial transient, and the hb is first solved with just that tone, and then the additional tones are added to the hb solve. Usually, the expectation is that the first tone is the most nonlinear (it's quite unusual to use 3 square waves with harmonic balance - not really its strength given that you would need many harmonics to resolve them well, and the product of 3 high-harmonic tones will be expensive to solve).

If all three had been enabled, then the transient assist would have to be over at least one cycle of the common frequency of the three frequencies (1MHz in this case). That means it would need to use the last 1us of the initial transient to be useful (and it would need to be more than 1us long) because otherwise there would not be any transient data that it could do an inverse FFT over to form the initial values for the harmonic solution. Since most of the time the tones in HB are not harmonically related, this wouldn't be useful very often - so having just a single tone to aid the first (most nonlinear) tone is a realistic compromise.

Andrew 

Hi Andrew, thanks so much for the detailed explanation. Then I wonder in such cases where 3 or more square waves are involved in a testbench, what analyze would you recommend to use in a mixed signal design? maybe transient then do FFT? or any other analyzes?

It rather depends on what you are trying to measure. What is the system you are simulating and what are you trying to measure?

Andrew

I am trying to design a RF DAC, which takes digital signal at the input and generate a RF signal at the output with the help of a clock signal. Those are the three square wave signals in my testbench. So the input is a baseband signal (fBB) passing through an ideal ADC (sample frequency fs) to generate the input signal that the RF DAC needs. Then the RF DAC takes a clock signal (fRF), which in this case, is an 8G square wave. So the function is like a DAC but also does up-conversion. At the output, I measure things like output power and linearity, such as IM3, OP1dB, etc.

The challenge is likely to be whether 11 harmonics are enough with the real circuit. You may be better off (since fs and frf are harmonically related) to just do a 2-tone simulation with 4x as many harmonics of fs (that would cover frf too). With 11 harmonics of each, your problem size is 23*23*23 (2*harms1+1)*(2*harms2+1)*(2*harm3+1). If you used 11 and 44 (say) then you'd have a problem size of 23*89 which is a factor of 6 smaller. If you need to increase the harmonics it will scale even better.

The worst case is to run a transient (but then you'd need to run transient over the common frequency) and do an FFT.

A lot of this will boil down to the practicality of simulating a realistic circuit. There's no simple answer. The circuit may be small enough you can run with a 3 tone HB with lots of harmonics? I'd probably start with HB and see how you get on!

Andrew

The challenge is likely to be whether 11 harmonics are enough with the real circuit. You may be better off (since fs and frf are harmonically related) to just do a 2-tone simulation with 4x as many harmonics of fs (that would cover frf too). With 11 harmonics of each, your problem size is 23*23*23 (2*harms1+1)*(2*harms2+1)*(2*harm3+1). If you used 11 and 44 (say) then you'd have a problem size of 23*89 which is a factor of 6 smaller. If you need to increase the harmonics it will scale even better.

The worst case is to run a transient (but then you'd need to run transient over the common frequency) and do an FFT.

A lot of this will boil down to the practicality of simulating a realistic circuit. There's no simple answer. The circuit may be small enough you can run with a 3 tone HB with lots of harmonics? I'd probably start with HB and see how you get on!

Andrew

Thanks so much Andrew!