How to measure electrical impedance with just 2 references: R and f

Impedance measurement is one broad topic. Traditional methods of measuring the impedance may usually include AC voltage or current reference, resistance references and time base. In my approach I chose to minimize reliance on absolute references like Voltage (Volts) or Current (Amperes) and make more use of less costly references of Resistance(Ohms) and Time(Seconds). It is much easier to rely on the value of off-the-shelf 0.1% accurate resistor with very high confidence. The accuracy and stability of low cost frequency sources like quartz oscillators is also well known and understood.

It is possible to rely on only these to R,Ohm and f,Hz to start designing basic fully capable Impedance Meter. Ohms Law describes Resistance as a ratio of Voltage over Current. The Law, when generalized for AC defines Impedance Z (complex pair of Resistance R and Reactance X) as ratio of AC Voltage to AC Current. The key word is "ratio". There is no need to know exact absolute value of Voltage and Current, the only needed value is just the ratio.

Let output amplifier apply unknown AC voltage to device under test (R1=DUT), which is grounded through known reference resistor (R2=REF). And say, voltage at DUT will be some observed value V1 and voltage on REF will be some observed value V2. Since AD converter has its own voltage reference (again: with unknown absolute value), we can treat V1 and V2 as observations relative to unknown internal Vref.

The only known value is R REF. So, ratio of V1/V2 will be proportional to R DUT/R REF, because they are connected in series. So it is possible to calculate R DUT, if experimenter knows V1, V2 and REF, and does not know absolute value of Vref , absolute current, absolute voltages.

This approach is ratiometric. And as long as absolutely accurate voltage and current is not in the picture, there is no need to use high cost references, traceable though certified laboratories. Highly confident impedance measurement requires only R and Time.