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Simulators >> RF Simulators >> Questions about positive frequency and negative frequency in PSS and PAC Analyse
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Message started by donalma on Aug 19^th, 2014, 12:16am

Title: Questions about positive frequency and negative frequency in PSS and PAC Analyse
Post by donalma on Aug 19^th, 2014, 12:16am

Hi~
I am now using cadence to design mixer. Spectrum is analysed by setting PSS, but only positive spurs(magnitude and phase information) are shown in results.

First question is whether negative frequency can be shown with PSS analyse?

Then,I check the bandwidth of the down-conversion mixer by utilizing PAC Analyse. I set my mixer with a 13GHz LO frequency and a RF frequency range from 1GHz to 30GHz. After that, the mixer would translate the frequency range to -12GHz to 17GHz. So, I ploted the voltage gain from the RF port(1GHz-12.99GHz&13.01GHz-30GHz) to the IF port(-12GHz--10MHz&10MHz-17GHz) with the help of PAC Analyse.The Figure of 'bandwidth' is shown below.

Here is my second question. Is this method used to test the bandwidth of mixer convincing?

On the other hand,'negative bandwidth'and'positive bandwidth'in this figure are asymmetric. In my opinion, positive bandwidth should equals negative bandwidth in spectrum, since we have cosωt=1/2(exp(jωt)+exp(-jωt)) and sinωt=j/2(-exp(jωt)+exp(-jωt)).

My third question is whether this ‘negative and positive bandwidth’ from PAC analyse is the same conception as what we normally think about negative bandwidth and positive bandwidth?

Hoping for ur xplanation pls.
:) :)

Title: Re: Questions about positive frequency and negative frequency in PSS and PAC Analyse
Post by aaron_do on Aug 19^th, 2014, 7:26am

Hi,

a couple of years ago I might have been able to answer this better, but anyway from memory...

physically realizable signals are always symmetric in magnitude about zero frequency. So the negative frequency is redundant. You can convert the magnitude and phase information into real + complex. The real part is evenly symmetric about zero frequency and the complex part is oddly symmetric about zero frequency.

The PAC plot you showed is the voltage gain plotted versus frequency (as you pointed out). It is not a broadband signal waveform. The asymmetry arises because of your RF bandwidth, not your IF bandwidth. You could try and "center" your LO about the RF resonant frequency, but it still wouldn't be perfectly symmetric.

When you say "positive bandwidth" and "negative bandwidth", I assume you are talking about baseband signals. Baseband signals can be asymmetric about zero frequency because they are a combination of two signals, one of which is the I channel and the other is the Q channel. So the baseband signal that you plot is I + jQ and it isn't physically realizable.

hope it helps,
Aaron

Title: Re: Questions about positive frequency and negative frequency in PSS and PAC Analyse
Post by Ken Kundert on Aug 19^th, 2014, 10:55am

SpectreRF has no difficulty working with negative frequency. By default it generally converts negative frequency signals into positive frequency signals before displaying them using the complex conjugate. You can control whether it performs this mapping, and whether to use input or the output frequency as the X-axis using the freqaxis setting.

I have no idea what you are talking about when you talk about positive and negative bandwidth.

-Ken

Title: Re: Questions about positive frequency and negative frequency in PSS and PAC Analyse
Post by donalma on Aug 21^st, 2014, 8:22pm

Thanks for your kind answering~
As you explain that baseband bandwidth can be presented as the from of I+jQ, where 'I' stands for 'I channel' and 'Q' stand for 'Q channel', can I regard 'I channel' as the Real part and Q channel as the Image part in BB bandwidth?
If so, bandwidth can be transfer into the form like A*exp(jθ), where A stands for amplitude, while θ stands for Phase information. When we refer to bandwidth symmetry, are we talking about the symmetry in 'A' without concerning about 'θ'?
Thanks.
Donal

Title: Re: Questions about positive frequency and negative frequency in PSS and PAC Analyse
Post by aaron_do on Aug 22^nd, 2014, 12:16am

Hi,

short answers, 1) yes, 2) no.

The thing is that bandwidth is a measure of how much of the frequency spectrum a signal occupies. Basically I think Ken was implying that it is a scalar quantity, so you're using the wrong terminology. I simply assumed that you were talking about the spectrum of a baseband signal.

The signal is contained in two channels, the in-phase channel, I, and the quadrature-phase channel, Q. For transmission, the I channel modulates one phase of the RF carrier, and the Q channel modulates a 90 degree phase shifted version of the carrier, and the two are summed together. For the purposes of mathematical manipulation, I believe that you can represent the two channels as real and imaginary parts.

Again, "bandwidth" is not transformed, the signal itself can be represented as a magnitude, A(f), and a phase, θ(f). The I-channel by itself is symmetrical both in magnitude and phase about zero frequency (phase might have rotational symmetry, I can't remember and I'm lazy to check). The Q channel by itself is also symmetric both in magnitude and phase. The combination I+jQ is NOT symmetric either in magnitude or phase. However, there is no part of the physical design where the signal I+jQ can be represented by a single voltage. It is just a mathematical representation and not physical. I and Q are not combined until they modulate a carrier. The modulated carrier is a real, physical signal, and it's spectrum is symmetric both in magnitude and phase.

best regards,
Aaron

Title: Re: Questions about positive frequency and negative frequency in PSS and PAC Analyse
Post by donalma on Aug 22^nd, 2014, 12:49am

Thanks for your suggestion~
I have just tried, it's just like what you advised.
thanks again^-^
donal