# AD5933 Feedback and Calibration Resistance

I'm making an AD5933-based circuit where I'm measuring the change of impedance. Based on the application note on how to calibrate the device for different impedance ranges, I see the formula is the following:

Since I am only interested in the change of capacitance (that is my unknown impedance), would it be possible to replace RFB with a capacitor? If so, what would the formula be? How do they arrive at the formula for RFB? I see in the circuit diagram its just a feedback placed after the unknown impedance. So in principle it should be possible to use a capacitor, right? And would it also be possible to replace RCAL with a capacitor? I know the datasheet mentions "Do Not Calibrate the System with a Complex Impedance", so perhaps RCAL has to remain?

$R_{FB}$ is part of a current to voltage amplifier. $R_{FB}$ must be selected to keep the signal below $V_{DD}$. Replacing it by a capacitor will change the function of the amplifier, so there is no assurance that the circuit will work as expected. This will also remove the DC part of the signal, and the IC probably needs it since it specify a maximum for the measurable impedance.
What you can do is calibrate with $Z_{ω}=R_{CAL}$ then swap it with a capacitor. The part have a maximum impedance limit so you may have to put that capacitor in parallel with a known resistor. If you are only interested in the chnage in capacitance rather than the absolute value, you could make a RLC resonator with the varying C, measure its resonance frequency with that IC, and forget about callibration.
• I think you have to electrically swap it. Put $R_{CAL}$, calibrate, then replace it by the capacitor (plus an resistor if needed). Maybe you could even keep $R_{CAL}$ all the time, just add the capacitor once you calibrated, and use math to find the impedance of the capacitor alone. Dec 17 '17 at 9:44
• The data sheet specify that $R_{FB}$ must be picked to keep the signal within the ADC range: "The AD5933 system gain settings need to be chosen to place the excitation signal in the linear region of the on-board ADC.", p19. If you replace $R_{FB}$ by a capacitor then the DC voltage of the RFB pin may not be set by anything inside the part, and could go outside the ADC range. Also, if you look at the block-diagram, replacing $R_{FB}$ by a capacitor create an integrator with transfer function $\frac{v_{ADC}}{v_{out}}=-\frac{C_{target}}{C_{FB}}$. Dec 18 '17 at 11:58