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# [SOLVED]Complex Filter

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#### fhongjin

##### Newbie level 4
Hi，
I’m trying to simulate a complex filter recently and I am having a hard time finding a way to combine the outputs (Q and I). I am using two ac sources as inputs and there are 90 phase shift between them. But I don’t quite understand how to interpret the outputs. Is there a way to plot the frequency response of the filter?

You have apparently knowledge about filter function that you don't share yet, e.g. that it's expected to be fed by an IQ signal. You also don't tell about filter usage.

If you analyze it as blackbox with two inputs and outputs, is each output a function of both outputs?

Hi，
I’m trying to simulate a complex filter recently and I am having a hard time finding a way to combine the outputs (Q and I). I am using two ac sources as inputs and there are 90 phase shift between them. But I don’t quite understand how to interpret the outputs. Is there a way to plot the frequency response of the filter?

Why do you want to "combine the outputs"?
And what do you mean with "Is there a way to plot the frequency response"?
When you use the correct input signals (phase difference 90deg), you will of course observe two output signals, which can be displayed and analyzed separately.
Which kind of frequency-dependence do you expect?
And then you can decide if it makes sense to "combine" the two signals.
--- Updated ---

Some time ago I have analyzed such a filter consisting of two first order lowpass stages. Feeding both inputs with two equal sinusoidal signals (with a phase shift of 90eg) the result was as expected:
A SYMMETRICAL bandpass response at both outputs (with different phase responses).
When we simply add both output signals we get a similar response with another (larger) amplitude and a shifted phase response.

Last edited:

Why do you want to "combine the outputs"?
And what do you mean with "Is there a way to plot the frequency response"?
When you use the correct input signals (phase difference 90deg), you will of course observe two output signals, which can be displayed and analyzed separately.
Which kind of frequency-dependence do you expect?
And then you can decide if it makes sense to "combine" the two signals.
Hi LvW,
And yes I did get 2 output signals. But I don’t know how to analyze the outputs. For example, if I want to see the bandwidth of a normal low pass filter, I just need to do an AC analysis and plot its frequency response right? However, I don’t know how to visually see the bandwidth of a complex filter like we normally do. Could you please suggest a method for getting the bandwidth, gain,IRR of a complex filter?

You have apparently knowledge about filter function that you don't share yet, e.g. that it's expected to be fed by an IQ signal. You also don't tell about filter usage.

If you analyze it as blackbox with two inputs and outputs, is each output a function of both outputs?
Hi Fvw,
The filter I’m designing is used in an RF receiver to filter out the image signal. And I fed an IQ signal to the filter. I think the input signals should be quadrature so I set a 90 phase difference between the two. I got 2 output signals and I don’t know how to analyze them. Could you please suggest a way in which I can get the BW, gain, IRR of the filter?

Thank you!

Hi LvW,
And yes I did get 2 output signals. But I don’t know how to analyze the outputs. For example, if I want to see the bandwidth of a normal low pass filter, I just need to do an AC analysis and plot its frequency response right? However, I don’t know how to visually see the bandwidth of a complex filter like we normally do. Could you please suggest a method for getting the bandwidth, gain,IRR of a complex filter?
You confirm that you "get 2 output signals". Now - what do you mean with "dont know how to analyze..."?
Do you see a bandpass response in each output signal (ac analysis) ?
What is the problem to determine the corresponding bandwidth and amplitude?

You confirm that you "get 2 output signals". Now - what do you mean with "dont know how to analyze..."?
Do you see a bandpass response in each output signal (ac analysis) ?
What is the problem to determine the corresponding bandwidth and amplitude?
I got two outputs but they are low pass. I didn’t see the shift of the lowpass filter. That’s why I am confused. Do you get two bandpass response on each output ports if you feed two quadrature input signal?

There's no shift in the filter, the shift is, presumably, on your two input signals. There are cases where you feed a real frequency input which gets applied to two multipliers to generate the I and Q signals before the filter, but I think in your case you've already got I and Q, correct? Is your complex filter really a "complex" filter, or two separate real filters?

And which is it, low pass or bandpass?

There's no shift in the filter, the shift is, presumably, on your two input signals. There are cases where you feed a real frequency input which gets applied to two multipliers to generate the I and Q signals before the filter, but I think in your case you've already got I and Q, correct? Is your complex filter really a "complex" filter, or two separate real filters?

And which is it, low pass or bandpass?
There's no shift in the filter, the shift is, presumably, on your two input signals. There are cases where you feed a real frequency input which gets applied to two multipliers to generate the I and Q signals before the filter, but I think in your case you've already got I and Q, correct? Is your complex filter really a "complex" filter, or two separate real filters?

And which is it, low pass or bandpass?
Hi Barry,

To my knowledge, a complex filter moves a real LPF to the right to filter out image signals. I applied AC signal to Iin and Qin. The two input signals have a 90 degree phase difference. Then,I got Iout and Qout from AC analysis in Cadence. And both of the outputs showed a lowpass frequency response.
I read several paper and I think they kind of “combine” the output signals. The correct response should be something like this:

The problem is I don’t know which analysis should I run to “combine” Iout and Qout and get the frequency response like this.

To my knowledge, a complex filter moves a real LPF to the right to filter out image signals. I applied AC signal to Iin and Qin. The two input signals have a 90 degree phase difference. Then,I got Iout and Qout from AC analysis in Cadence. And both of the outputs showed a lowpass frequency response.
I read several paper and I think they kind of “combine” the output signals. The correct response should be something like this:
The problem is I don’t know which analysis should I run to “combine” Iout and Qout and get the frequency response like this.
Perhaps you should show us your circuit diagram.

When you combine two 1st-order lowpass stages to a complex (multiphase) filter the result would be AT EACH of the two output nodes a bandpass response - provided you feed both inputs with two Q-I signals.
In particular, this gives a bandpass response which is - in contrast to the "classical" bandpass - fully symmetrical with respect to the center frequency.
You simply can combine (add) both output signals - and the result again is a bandpass with a larger amplitude at the same mid-frequency.

Perhaps you should show us your circuit diagram.

When you combine two 1st-order lowpass stages to a complex (multiphase) filter the result would be AT EACH of the two output nodes a bandpass response - provided you feed both inputs with two Q-I signals.
In particular, this gives a bandpass response which is - in contrast to the "classical" bandpass - fully symmetrical with respect to the center frequency.
You simply can combine (add) both output signals - and the result again is a bandpass with a larger amplitude at the same mid-frequency.

I am now using one pair of signals (one for I and one for Q) and here is the single-ended circuit diagram just as an example. mine are fully differential

OK - my circuit was very similar to yours. It should work when the Q-signal lags the I-signal by 90deg.
In the other case, (I lags Q) we get a very low output (image suppression).

The 3dB bandwidth of each of the two outputs is twice the 3db-corner frequency of the lowpass.

There is one additional point that just came into my mind:
The whole circuit is, of course, a LINEAR circuit. Therefore, the inverter at the output of the 1st opamp must be a LINEAR inverter (opamp). In your circuit diagram it looks as you have used a digital unit.
Of course, this cannot work.

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