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I am currently trying to understand the influence of the number of windings and load resistor on the current output of a current transformer (CT). My schematic consists of a CT, a load, a divider after the load to get proper voltage levels, and a half-bridge rectifier with a capacitor after the load to supply schematic nodes.

The supplied current from the capacitor is very low and its influence is negligible. I am using custom current transformers with known winding ratios.

I have the following questions:

  1. Does increasing the number of windings in the secondary (let's say multiply by 2) make the core saturate at a higher primary current, since the secondary current is reduced? Also, does the resistance seen by the primary lead to a reduced voltage drop in the primary?
  2. If I increase the number of windings, won't it affect the overall saturation power, since that rating is a function of the core? (let's say normal primary currents are from 40-100 A; I'm seeing current distortion on the load resistor at 80 A (saturation) and rarely 500 A on primary can occur). To be more clear: I want to know if dissipated power at such a 500 A current spike doesn't correlate with the number of windings or correlates very little?
  3. If I reduce the load (let's say divide by 2) then will the primary current at which the core saturates be higher?
  4. Is it possible to plot the dependence of the output voltage on the load versus primary current at several points, then interpolate it and be sure that when knowing the load and the primary current, you can match it with the voltage in the secondary?

I can provide any additional information and take oscillograms if needed.

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If we neglect losses and leakage inductances and assume linearity, a transformer with a sinusoidal input and a resistive load can be modeled as an inductive reactance \$X\$ in parallel with a resistance \$R\$. Here, \$X\$ is the reactance of the primary, leaving the secondary open, and the \$R\$ is the resistance of the burden attached to the secondary referred to the primary side. That is, $$R = \frac{R_{burden}}{n^2}$$ where

$$n=\frac{N_{secondary}}{N_{primary}}$$

is the turns ratio.

schematic

simulate this circuit – Schematic created using CircuitLab

If I have done my math correctly, the modulus of the impedance of such a circuit is:

$$|Z| = \frac{RX}{\sqrt{R^2 + X^2}}$$

and the voltage developed across the primary is related to the current through the primary by:

$$V = I\frac{RX}{\sqrt{R^2 + X^2}}$$

Here, \$I\$ is the primary current, and \$V\$ is the voltage that would be induced under the assumption that the core is not saturated and is "linear".

Does increasing the number of windings in the secondary (let's say multiply by 2) make the core saturate at a higher primary current, since the secondary current is reduced? Also, does the resistance seen by the primary lead to a reduced voltage drop in the primary?

Questions 1,2 mean constant burden.

Changing the number of windings in the secondary will not change \$X\$, the inductive reactance of the primary. However, it will change the burden resistance as referred to the primary side. Multiplying \$n\$ by a factor two will cause \$R\$ to decrease by a factor of 4. If \$R << X\$, which it is likely to be in "normal" operating conditions, then \$|Z| \approx R\$, so \$|Z|\$ will decrease by some factor slightly less than 4.

Since doubling the number of secondary turns will cause \$|Z|\$ to decrease (by some factor between 1 and 4), the primary current necessary to saturate the core will increase (by the same factor).

If I increase the number of windings, won't it affect the overall saturation power, since that rating is a function of the core? (let's say normal primary currents are from 40-100 A; I'm seeing current distortion on the load resistor at 80 A (saturation) and rarely 500 A on primary can occur). To be more clear: I want to know if dissipated power at such a 500 A current spike doesn't correlate with the number of windings or correlates very little?

Increasing the number of turns in the secondary winding, while keeping the burden resistor the same, will increase the power transferred to the secondary, when the primary voltage is sinusoidal and at saturation level. Again, if \$R << X\$, that factor will be approximately \$n^2\$, but the factor decreases as \$\frac{R}{X}\$ increases.

Current spikes are another matter. The transformer model I have been using assumes a sinusoidal input. If I get time soon, I will attempt to give an analysis of saturation in terms of a history of instantaneous primary currents. However, for the moment, I will omit this part of the answer. Perhaps someone else can answer it first.

If I reduce the load (let's say divide by 2) then will the primary current at which the core saturates be higher?

Yes, if you reduce the load (burden), but leave the turns the same, the impedance seen by the primary will be lower. Thus, there will need to be a larger primary current to develop the same voltage across primary. It is the volt-seconds across the primary during a cycle that causes saturation. So, with a lower impedance seen by the primary, it will take a larger primary current to cause saturation.

Is it possible to plot the dependence of the output voltage on the load versus primary current at several points, then interpolate it and be sure that when knowing the load and the primary current, you can match it with the voltage in the secondary?

If \$R\$ and \$X\$ are maintained constant, and the B-H curve of the core is in the "linear" region, then the voltage induced in the primary will be directly proportional to the current. Again, the formula for a sinusoidal input (if I have done the math correctly) is:

$$V = I\frac{RX}{\sqrt{R^2 + X^2}}$$

Saturation of the core depends on the volt-seconds across the primary in a cycle. If the current is periodic and a given (for example sinusoidal or square), and the frequency is a given, then saturation will occur when the peak or rms voltage across the primary reaches some given value (which depends upon frequency, waveform, and the magnetic core).

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  • \$\begingroup\$ Questions 1,2 mean constant burden. I was testing two defferent custom CTs with 1:5000 and 1:2200 ratio and found that 2nd CT saturates first (have lower transformer ratio) but it passes less power at 50A to same R (already saturated at that current) then slightly saturated CT with 1:5000. Also i wanted to know which CT have more risk to break down at some primary current if they are heavilly saturated at that current. At last question i was curious if i can think of it as a transistor and knowing "transfer characteristic" have ability to draw V or I on secondary knowing I primary, burden,core \$\endgroup\$ Apr 6, 2023 at 13:38

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