Isolated voltage measurement with an ACS37800

Question

I am measuring 250VAC with an ACS37800. It happens to be a PWM based output of a TRIAC. For testing purposes, I am varying the duty cycle and input voltage to validate the measurement circuitry. My circuitry is very similar to the circuitry in the datasheet (first page of datasheet.)

As I vary the duty cycle of my TRIAC (one second period,) the expected output voltage is input voltage * sqrt(duty_cycle). I am measuring that output voltage. I have an isolation transformer (a 1:1 style,), and a two pole variac (schematic below.)

^{simulate this circuit – Schematic created using CircuitLab}

When I run the autotransformers with an output of 120V, everything looks as expected. When I run the isolation transformer, there is an offset for 0 output (like 80volts,) and the voltage at full on is much lower. The weird part is when connected without any transformer, my measured values are actually inverted (as if I am measuring the voltage across the TRIAC, but I am not.) Instead of voltage vs duty cycle looking like f(x) = 300x, it looks like f(x) = 300(1-x). I do know that the external circuitry which essentially connects earth ground to the DC ground plays a role. I am trying to simulate this effect in LTspice and have not been successful.

How can this be simulated in LTspice? My assumptions of a resistance between earth ground and digital ground so far only results in f(x) = x*c, where the constant c changes.

Here is a representative schematic

^{simulate this circuit}

Answer 1

I found a solution to my problem. I split the 4.2k resistor in half, grounding the junction between them instead of one end.

Answer 2

It called phase angle control, not PWM.

Source of the image:

And of course it is not linear as you say

f(x) = x*c,

rather a trigonometric/square function:

$$V_{load_{RMS}} = Vpeak *\sqrt{\frac{2 \pi - 2 \varphi + sin2 \varphi}{4\pi}}$$

EDIT:

The IC is for energy metering, so it has to be connected on 50/60 Hz voltage, not a load voltage. The current measures the load current, then you get a power/energy value.