nano_voltmeter Files

To create the greatest possible precision in a voltmeter four factors need to be controlled; gain, offset, bandwidth and
input resistance.
Three of these factors are controlled by using a well proven technique, a chopper amplifier with feedback. By using a
chopper, the input resistance approaches inifinty at null and the feedback eliminates gain and offset errors.
Bandwidth is controlled by limiting the frequency bandwidth of the signal fed back to the chopper.
Under null conditions no current is being drawn from the input source and the whole system acts a charge balance.
Balancing the charge is done by exclusively using MOSFET devices for switching and amplification.
Offset is eliminated by never introducing it into the circuit. Instead of amplifying and rectifying the chopper signal
prior to feedback, the chopper fundamental harmonic amplitude and phase are measured digitally using auto correlation.
An oversampling ADC is used as a detector. It's input is biased at half it's reference voltage and it is effectively AC
coupled so its input offset is irrelevant. The sampled data is correlated with sine and cosine values of the chopper
frequency with the sine corresponding to the complex and the cosine the real part of the chopper fundamental harmonic
vector.
The absolute value of the vector is proportional to the magnitude of the error signal and the sign of the cosine term
is used to determine the relative polarity between the input signal and feedback signals.
There are two major advantages with this method, no DC error term is introduced and the bandwidth is centered around the
chopper frequency and can be made arbitrarily small. There is no DC path through the system. By breaking the DC chain,
problems with DC leakage, thermal offsets and similar problems are eliminated.
The feedback must also be offset free to maintain precision. The simplest way to do this is use a PWM with a passive RC
filter. This combination is effectively a charge metering device with the PWM alternately adding and subtracting charge
over time to leave a net charge which balances out the input voltage. A multistage RC filter is used to reduce ripple
and the PWM frequency is a harmonic of the chopper frequency so the auto correlator will null any residual ripple. This
doesn't introduce any inherent offset and the precision is determined digitally. No precision resistors or capacitors
are required which keeps the cost very low.
High resolution PWMs are very slow. To increase resolution, two PWMs are used in series. The output of one PWM is used
as the input of the second PWM. Because a PWM is a multiplier, one PWM acts as a range switch for the other PWM and the
overall response is logarithmic.
MOSFET transistors are used to implement both the chopper and PWM switches. One problem with MOSFETs is that the gate
capacitance will inject charge from the gate drive into the circuit being switched. This is not a problem if the charge
injected when the MOSFET is turned on and the charge removed when the MOSFET is turned off are the same. If this is the
case, the total charge in the system remains balanced and no offset is introduced.
The problem is that if one chopper switch is turned off and the other chopper switch turned on before the charge has
time to dissipate into the circuit, the charge will be removed when the second switch activates which will upset the
charge balance.
To prevent this, a delay is introduced between the change of switch states to allow time for the charge to dissipate.
Another problem is that with the chopper switches, the chopper drive signal is synchronous and indistinguishable from
the chopped input voltage. The amount of signal injected is proportional to both the switching frequency, and the
device capacitances. This cannot be eliminated, but greatly reduced by using a low chopping frequency.
The switches are also turned on and off as rapidly as possible. This concentrates the energy into the higher harmonics
of the chopper frequency which are eliminated by the auto correlator.
A 10 Hz chopper frequency is used because it is a subharmonic of all common power line frequencies. The ADC sampling is
done at exactly 1 kHz to maintain synchronicity with the chopper.
Auto correlation is done by multiplying the input signal by the reference signal and then integrating the product.
Because multiplication is commutative, integration can be done first by summing multiple samples and then multiplying
the integrated samples to reduce processing time. Also, double buffering is used so that while new samples are being
collected, the previous samples will be processed.
Filtering is done using a single integrator because this requires little computation and is easy to stabilize.
A commodity CMOS op-amp is used to implement a multistage AC amplifier. Because of the low chopper frequency, a very
large series capacitance is required after the chopper and between the amplifier stages. The input capacitor has to
charge and discharge to the common mode voltage at the chopper input through the amplifier feedback resistor which is
also quite large.
To speed up this process, software controlled switches are placed across the feedback resistor to greatly reduce the
charge and discharge times.
To minimize noise, the integrator time constant has to be very large which greatly increases the time for the circuit
to balance. Although the amplitude of the null error is not known, the polarity of the null error is known every
chopper cycle because the phase of the error term is independent of amplitude. By using the polarity as a reference and
using a binary search technique, the integrated value can be preset and a null obtained relatively quickly.
The intent of this voltmeter is not to set speed records, but instead to demonstrate how to obtain the highest possible
precision and accuracy using the least expensive means possible. Although very slow, it's possible to measure accurately
into the picovolt and possibly the femtovolt range.