Fig. 1: A simple measurements system using voltage to frequency conversion
The accuracy of the system strongly depends on the properties of the voltage controlled oscillator (VCO). A typical example of such a VCO is shown in the following figure:
Fig. 2: Example of a VCO
The input voltage Vin is converted into a current by OP1, M1 and R1.
I = Vin/R1
This current is used to charge C1 and C2 until the voltage reaches Vref leading to a charge time of:
T = C1*Vref/I = C1*Vref*R1 / Vin
Assuming both capacitors are equal the frequency of the oscillator will be:
f = 1/(2T)
f = Vin / (2*C1*R1*Vref)
So if it is so easy why do most voltmeters use more complec circuits?
The problem is the production tolerance of R1 and C2, C2. Mass production semiconductor process parameters typically allow +-20% of tolerance for resistors and capacitors. So the circuit will have an initial tolerance of +-40%.
There are further error sources such as propagation delays of COMP1, COMP2 and RSFF.
So this circuit requires trimming at wafer sort.
Resistance of semiconductors (R1) usually has a temperature coefficient in the rang of +-0.1%/K to as bad as +-0.3%/K. Even if the device is trimmed a wafer sort due to temperature coefficients the circuit will probably never become more accurat than +-10% unless it is operated at a constant temperature.
Thermostats are expensive, require warm up time and draw a lot of current.
The main application of this kind of circuit are in the loop signal conditioning where the loop gain is high enough to compensate gain errors of a factor 2 or more (For instance carrying a signal from one supply domain to an other by AC coupling or by opto couplers).