# Correlation between saturation of high current (power) transformer core and load

In an experiment I need high ($>600A_{max}$ or $1200A_{pp}$) AC currents in a range from 400Hz to 4kHz. The load is simply a short circuit. For this purpose i use a class D audio amplifier and a transformer with a capacitor in series, so I create a LC series resonant circuit. The frequency is set as it is needed to get resonance.

The transformer has 74 primary windings and 1 (2) secondary windings of HF flex cable. This HF flex cable has a length of ca 1.2m and is intertwined so that the inductance is rater low. The short circuit is made over a ca 5cm long copper bar, there applies the skin effect and this short pice of copper gets pretty hot.

The core of the transformer are two C shaped ferrites that are lashed together so i can't exclude a minimal air gap (but it has to be rater small). The exact data of the core is not present at the moment.

This is just a quick experiment for me and i used spare parts i found... Now i get two interesting effects and i don't understand the reason behind them:

(The same capacitor are used for (1) and (2) the frequency is set to resonance and differs for a few Hz from (1) and (2))

Note: i can't remember the exact numbers, they should only provide a reference point.

(1) On a first step I used 1 secondary winding. I get a primary current of ca $5A_{max}$ ($10A_{pp}$) and a secondary current of $350A_{max}$ ($700A_{pp}$). If i go up future with the input current the shape of the current goes from nice $sin$ to a triangle shape. The output current stays $sin$ for a bit and changes then also.

(2) On a second step I use 2 secondary windings. I get a primary current of $14A_{max}$ ($28A_{pp}$) and a secondary current of $500A_{max}$ ($1000A_{pp}$). If i go future with the input current the secondary current gets a strange shape and short after that the primary current gets peaks. The typical signs of saturation...

My question: Why does the primary current gets a triangle shape in (1). The effect from (2) is clearly saturation. If (1) is also a saturation effect, why does it rise with $5A_{max}$ and in (2) at $14A_{max}$ isn't the magnetic field only dependent from the product of $I_{prim}\cdot N_1$ and the saturation of the material constant for a fixed frequency? Is there a load dependency of the magnetic field in the core?

Note: the amplifier does not saturate (nor in output voltage, or current). It has plenty of power left...

• The slope of triangle current is dI/dt which is related to Class D voltage squarewave by dI/dt=V/L – Tony Stewart Sunnyskyguy EE75 Sep 7 '16 at 0:08
• The PWM frequency of the amplifier is at least 40kHz, but my triangle wave has the same frequency as the sinus input signal. The output voltage of the amplifier has also a nearly nice sinus form and not a constant voltage. – B.Hazza Sep 7 '16 at 6:55
• primary saturation depends on V/f for no load and indicated by harmonic content of current – Tony Stewart Sunnyskyguy EE75 Sep 7 '16 at 17:26
• vias.org/crowhurstba/crowhurst_basic_audio_vol2_069.html – Bruce Abbott Sep 8 '16 at 22:20

why does it rise with 5Amax and in (2) at 14Amax isn't the magnetic field only dependent from the product of Iprim⋅N1 and the saturation of the material constant for a fixed frequency? Is there a load dependency of the magnetic field in the core?

Magnetizing current (and the resultant magnetic field in the core) is created by voltage across the primary winding's magnetizing inductance (Xm in the transformer equivalent circuit below). Since current in an inductor rises at a rate proportional to voltage and time, increasing primary voltage or reducing frequency will increase magnetizing current, driving the core into saturation if the voltage is too high and/or frequency too low. Putting a load on the secondary makes the primary draw more current to feed it, but this transformed current is separate from the magnetizing current and so does not directly affect saturation. However the increased primary current does cause a voltage drop across the primary winding's resistance (Rp) and leakage inductance (Xp). This voltage drop subtracts from the voltage across the magnetizing inductance, so a higher voltage and/or lower frequency is required to drive the transformer into saturation.

When you put a short circuit across the secondary the primary current becomes very high, causing a significant voltage drop in the primary. Putting two output windings in series causes higher current draw for a particular input voltage and frequency, increasing voltage drop and so requiring higher voltage and/or lower frequency (and therefore even higher current) to reach saturation.

• How obvious, shame on me.... Tank you!!! – B.Hazza Sep 14 '16 at 7:21

I can confirm that this phenomena was saturation of the core. Today I tried a bigger core and the triangle shaped wave form was gone and i could achieve currents of $>2000A_{pp}$.

I think the reason why the core saturated at (1) at $5A$ and in (2) with $14A$ is because with two windings the output voltage is bigger and with the same resistance of the (not ideal) short circuit there could flow a bigger secondary current ($500A$). This induced a bigger "counter" flux in the core what prevented the saturation. But then also this voltage was to small to overpass the resistance and the secondary current could not grow further. With that also the counter flux could not grow and the core goes into saturation.