# How is the lower voltage on a transformer calculated?

I was reading the data sheet for the LT8301 and laid on eyes on one of their example schematics. The input range (Vin) in the example states 2.7V-36V, and even gives measurements for when Vin = 5V. However, looking at the Sumida 12387-T041 inductor (T1) shows that the application voltage range on the primary size is 18V-42V. Presumably allowing less than 18V (i.e. Vin < 18V) enter the transformer is fine, otherwise Linear wouldn't give this example schematic.

So this begs the question: how is the lower voltage limit calculated, and at what point does the transformer no longer functions (output power on the secondary becomes insignificant (I realize this is a bit ambiguous, but I can't figure out how to word it differently))?

• If the input voltage is too low, you cannot reach the expected output voltage and current. Sep 19 '15 at 21:57

That lower voltage value is listed under the general heading "target application" and I'm sure if you dug deeper you'd find that target application and be able to show a circuit diagram then all would become obvious.

It also says (under that target application) that the output voltage is 5V yet the LT circuit shows 15 volts so you need to dig a bit to find that circuit.

The LT circuit is a flyback converter and the ratio of DC input to DC output voltage has very little to do with turns ratio and much more to do with duty cycle. For instance, the transformer (aka coupled inductor) in question is ratio 1:1 so, as far as duty cycle is concerned I'd expect input voltage to equal output voltage at 50:50 (this is a broad brush impressionist type remark of course) and if you do the sums (below) it is not that far off....

Input voltage range is 2.7 volts to 36 volts and this averages about 19 volts so having 15 volts at the output is "about" right (generalisms used with caution of course) for the mid range of input DC voltage.

Like I said earlier, it's a flyback circuit and duty cycle is king and basically turns ratio is the parlour maid: - She's the one at the back on the left and he's the one at the front calculating the duty cycle.

• Thanks for the response. I feel like I'm getting closer to the answer, but I'm not quite there yet. I think the problem is that I poorly asked the question. Let me ask differently. Why is there a minimum voltage listed on this transformer on Digikey? digikey.com/product-detail/en/PA3855.005NLT/553-2133-2-ND/… . How is it measured, and what does it mean if the voltage goes below this rated minimum? Sep 22 '15 at 3:16
• Somewhere there will be a circuit of a target application that uses this transformer (amongst other components) to produce a DC-DC converter circuit and, that target circuit works with an input voltage dc range of 18 to 42 volts. I did state this in my opening paragraph. That circuit I believe is one in the LT8301 data sheet i.e. if you use that transformer expect the whole circuit to cope with input voltages from 18 to 42 volts. Sep 22 '15 at 7:25
• Thanks for the clarification. I guess my question is more fundamental than this. Suppose I wound a transformer in my lab and wanted to sell in on Digikey, how would I find out what the minimum voltage of the transformer is? What are the necessary measurements and criteria required to report a final value? Presumably, given a sufficiently low voltage applied on the primary, the transformer would produce such a tiny current on the secondary that we would effectively consider the transformer as no-longer functioning. What is the threshold for "no-longer functioning"? Sep 22 '15 at 22:39
• @TRISAbits A transformer has no minimum operating voltage - it works on AC and therefore the instantaneous value of the voltage can be 0V. Neither is it a problem operating at extremely tiny RMS voltages like 1 nV! Sep 23 '15 at 7:40

As Andy Aka pointed out, transformers function at any input voltage, even voltages well below the minimum spec voltage. If the physics don't impose a limit, then how do manufacturers calculate the minimum voltage on their transformers?

I went and talked to a few FAE contacts I know and asked them how they calculated their minimum voltage ratings. Interestingly, no one had the same answer. It seems every company has a different method of qualifying their transformers, which confirms what Andy Aka was pointing out.

One of the most detailed answer said something along these lines (paraphrasing a lot here):

The minimum input voltage is calculated in function of the highest input currents and longest duty cycles which maintain the output voltage within its desired range.

There's a corollary to the statement above

The minimum input voltage calculation is dependent on the power supply topology which the transformer is intended to operate.

That is to say, the minimum voltage is calculated for a specific SMPS topology.

Using this method for calculating numbers, if I wound a transformer to operate in a flyback power supply, I would:

1. Figure the required output voltage and current, select the appropriate wire size for the output, and wind the output.
2. Figure out the input voltage range I want to support.
3. Run a simulation to see what the input current becomes for the highest duty cycle.
4. If the input current is too high, either change my output voltage/current requirements, or increase the minimum input voltage. Otherwise, select the appropriate wire size and wind the input.

This is just one method of calculating the minimum input voltage. As I said before, every FAE I talked with had a different method (some didn't even know).