Transformer: Number of turns om primary winding

I'm researching electromagnetism for a guitaramp project. I would like to experiment with different homemade transformers.

Find myself stuck trying to get a grip on the effect of the number of turns on the primary winding in relation to the risk of a saturated core. One the one hand more turns imply more inductance according to Inductance (L) = number of turns (N) times magnetic flux(Wb)/current (I). On the other hand it is well known that decreasing the number of turns on primary will increase flux density and the risk of saturation. I guess it must be the relation between number of turns and current that gives the answer, but find it hard to find good explanations. Anyone with a good advice?

• It's not the number of turns that's important, it's the total voltage that determines how much flux you will generate in the core. More turns indeed means more self-inductance, so with AC that limits the current that will flow but not the flux. – joe electro Nov 16 '18 at 9:07

I guess it must be the relation between number of turns and current that gives the answer

Correct - amps x turns is called magneto motive force and it's what drives magnetism and potential saturation. It's related to the magnetic field strength (H) by dividing MMF by the distance the flux path takes around the core so: -

$$\dfrac{MMF}{\ell_e} = H$$

And H is related to flux density (B) by the permeability of the core material: -

$$B = \mu\cdot H$$

So, too much flux density goes right back to having too many ampere turns.

For AC, the inductance of a transformer winding is proportional to turns squared so, if you double the turns you get 4 times more inductance and one-quarter the current for a given voltage/frequency. This generally means that more turns means less core saturation because although the turns might (say) double, the amps reduce to a quarter.

The picture below (hopefully and intuitively) explains how inductance is proportional to turns squared: - Anyone with a good advice?

That's dependent on the reader!

• Thank you for the response. Still trying to grasp it. If we double the turns inductance quardobles and current is reduced to 1/4. How come this doesnt mean that flux is constant? Your explanation relies on MMF being a product of current times turns. But what about induktion that is quardobled? – Søren Vestergaard Nov 14 '18 at 5:50
• MMF is current x turns. I’m not making that part up. More turns means less flux and less induced voltage per turn in the secondary but more turns means overall output voltage is constant. Ie turns ratio defines induced voltage in secondary relative to primary. – Andy aka Nov 14 '18 at 7:24
• Guess I have to dig more into the relation between current, flux and induction. What determines the current - inductance? Is flux proportional to current and turns? I am surprised that it is so difficult to find intuitive explanations on these relationships. Especially the relation between number of turns and the effect on current in the circut! – Søren Vestergaard Nov 14 '18 at 10:32
• Magnetization current (unrelated to primary referred load current) is related only to the magnetization inductance and that is why we wind so many turns - we try and keep inductance as high as we can to avoid core saturation. But, current in the primary is both mag current and secondary load (referred to the primary) current. It's not that hard once you get your head around it. – Andy aka Nov 14 '18 at 12:30
• Still reading. Now I dont understand how field strength/flux is proportional til N when inductance is proportional to N squared. As I understand it, induction works through magnetization of the core and can be described L=flux/current. How come this aspect of flux bieng proportional to N and indcutance being proportional to N squared is not more often described? Seem intuitively strange? – Søren Vestergaard Nov 15 '18 at 12:56

For a voltage sourced transformer, which most are, I always use Vt=NAB. Vt is your voltage time area on the primary. N is your primary number of turns, A is the minimum cross section area of the core and B is your peak flux. Voltage-time area makes good sense for SMPS but a bit less so for 50/60 Hz transformers, but see below.

Any current source or more likley a choke calculation it's LI=NAB. All units are again in SI. Your L can be written as L=Al*N^2, so you can simplify here depending on if you know your inductance or Al-value. You can derrive Al down to u for the material too and core geometry if you want.

For any sine wave input transformer, you can use Urms=4.44fNAB.

Aim for 1 T for any laminated steel and most iron powder cores and 0.3 T for ferrite.