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I would like to know does anyone know how to model the frequency dependent IQ imbalance. The frequency independent model is when gain and phase imbalance are just constant now assume that gain and phase are linearly changing.

The independent case is modeled as

$$\alpha x(k)+\beta x^*(-k) $$ where \$x^*\$ is the x complex conjugate and \$\alpha\$ and \$\beta\$ are related by cosine and sine relationship.

How can I make the FD IQ imbalance to add it to simulation as a distortion. I know this will happen when the filter in I and Q are different but is there any set of equations like the above case that models the frequency dependent case.

Voltage Spike
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math
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1 Answers1

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Add a low-pass filter to either I or to Q. I helped a chip debug, where the sideband suppression was only 20dB, because of imbalanced parasitic capacitance on the I or on the Q paths.

analogsystemsrf
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  • Can you elaborate about this a little bit.I am almost having the same question that I need to simulate this effect but wondering where to add the low pass filter and how mathematically model this? – user59419 Jul 12 '17 at 06:20
  • You need to run a transient simulation. Consider the standard balanced-mixer with differential LO port and differential RF port. And differential IF port (your output). Add enough LPF in any of the 4 input wires (LO, RF) to cause 10 degrees phaseshift. Pick R & C to not greatly load the source. After 10 degrees is understood, go for just 1 degree. And for just 0.1 degrees. When we achieved balanced on-silicon capacitance / metallization area AREA, we reached better than 50dBc sideband suppression. [ Not sure how to mathematically model this. ] – analogsystemsrf Jul 12 '17 at 12:58
  • how to model? What is the linear combination of sin(100 + 0 degrees) with sin(100 + 10 degrees)? If this feeds the RF port (the linear port) of a double-balanced mixer, then MATLAB code should be adequate to model that linear combination of 0 degrees and the phaseshifted version. – analogsystemsrf Jul 12 '17 at 14:12
  • Thanks for you response. Can you explain what you mean by linear combination of 0 and 10 degree shift sine. It is like product of sine and cosine using trigonometric identity. What should I do with that. I want to model in Matlab. Like the frequency dependent case that is well studied and there alpha and beta that are related by sine and cosine function. How can I relate the parameters here – math Jul 12 '17 at 15:30
  • Implement [sin(100T + 0 degrees) + sin(100T + 10 degrees)] as a trig conversion. – analogsystemsrf Jul 13 '17 at 03:45