transformers - diglet48/restim GitHub Wiki

The ideal transformer for e-stim applications has these specifications:

  • Isolation rating of $1500V$ or better.
  • Flat frequency response and low phase shift for frequencies $500Hz$ to $3000Hz$.
  • Low-ish DC resistance around $1 \Omega$ for the driving side.
  • A winding ratio between $1:5$ and $1:15$, the ideal ratio depends on drive circuit characteristics.
  • Saturation between $5,000V\mu s$ and $40,000V\mu s$. Higher values are dangerous.

Annoyingly, some of these specifications are rarely mentioned in the datasheets.

The winding ratio is the square root of the impedance ratio.

Measuring winding ratio and saturation

A simple test to figure out the winding ratio and saturation for your specific transformer.

Requires an oscilloscope and a few basic components, a voltage source, capacitor and pushbutton.

The idea is to generate a square waveform (here from 0 to 5V) with the pushbutton, measure the voltage response on both sides. The input is the low-voltage side, and the output the high-voltage side.

The winding ratio is the voltage ratio at the start of the pulse (about $37V / 5V = 7.4$). It differs from the datasheet winding ratio of 6.25, a common sight.

The saturation is the area under the yellow curve, about $0.25 Vs$ (volt-seconds), just count the number of squares. It scales by the cross-section of the core and (linearly) by the number of windings.

Estimate sturation from datasheet

The saturation (volt-seconds) can be estimated from the inductance and saturation current. Recall the basic RL-circuit squation.

$I(t) = \frac{V}{R} (1 - e^{-\frac{R}{L} t})$

The transformer reaches saturation at time:

$t = -\frac{L}{R} \ln({1 - \frac{I*R}{V}})$

We want to know $volt*seconds$, so multiply both sides by $V$

$Vt = -V\frac{L}{R} \ln({1 - \frac{I*R}{V}})$

If we select $V \rightarrow \infty$, we simply get:

$Vt = LI$

The inductance scales with the $\text{windings}^2$, and saturation current with $\frac{1}{\text{windings}}$, so to maximize $\text{volt}*\text{seconds}$, we want lots of windings.

Power supply transformers

Many readily-available transformers are created for switch-mode power supplies. These operate at a voltage of $230V$ and typical switching frequency of $200kHz$.

With 50% duty cycle, it follows that volt-seconds is $230V/200kHz*50% = 575V\mu s$. Not nearly enough for our purposes.

tests

Assortment of 230v transformers: