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# (Dry goods exchange) Calculation of air gap by formula of transformer

2023-11-04【Archive】

First, formula in converter

1) V=N*B*Ae/t.

V is voltage on coil;

N is number of coil turns;

B is magnetic flux density of core;

Ae is cross-sectional area on which core is wound

It's time.

The meaning of formula: in time t for a coil with N turns of wire, change in magnetic flux is N*B*Ae, and induced voltage is V.

Ampère's theorem: N1*I1+N2*I2...=H1*L1+H2*L2. In a constant magnetic field, line integral of magnetic induction B along any closed path is equal to algebraic sum of currents surrounded by closed path multiplied by magnetic permeability.

N1 is number of turns of coil 1 on winding core.

I1 is current on coil 1.

H1 is magnetic field strength of magnetic circuit = B/u0*ur, u0 is magnetic permeability of vacuum, ur is relative magnetic permeability of magnetic circuit.

L1 is length of magnetic field contour in core.

H2 - magnetic field strength of air gap of magnetic circuit=B/u0

L2 is length of core air gap.

B=u0*(N1*I1+N2*I2+...)/(L1/ur+L2).

Second, direct transducer

Waveform at maximum power

Oscillogram of magnetic flux density versus time t

In formula 1 (V=N*B*Ae/t), given that more turns, greater losses, and more magnetic circuit is required, therefore, number of turns should be chosen as small as possible, and B= should be chosen Bmax. V=N*Bmax*Ae/t1, find N and take an integer Ni from N as number of winding turns.

After choosing Ni, Bi=V*t1/(Ni*Ae) can be obtained at this time.

Formula Pass 2:

Bi=u0*(N1*I1-N2*I2)/(L1/ur+L2).

In a transformer, current direction of terminal of same name is opposite, so sign is opposite.

When the power is p, I2 is determined and I1=Bi*(L1/ur+L2)/(u0*N1)+N2*I2/N1 can be calculated.

Transformer input power=I1*V*D=0.5*Bi*(L1/ur+L2)/(u0*N1)*V*D+N2*I2/N1*V*T*D=0 .5* Bi *(L1/ur+L2)/(u0*N1)*V*D+p. can meet power requirement. Therefore, direct transformer does not need to adjust L2 value to meet power requirement.

3. Flyback transformer (intermittent)

Oscillogram of magnetic flux density versus time t

In formula 1 (V=N*B*Ae/t), given that more turns, greater losses, and more magnetic circuit is required, therefore, number of turns should be chosen as small as possible, and B= should be chosen Bmax. V=N*Bmax*Ae/t1, find N and take an integer Ni from N as number of winding turns.

After choosing Ni, Bi=V*t1/(Ni*Ae) can be obtained at this time.

Formula Pass 2:

Bi=u0*(N1*I1)/(L1/ur+L2).

In a flyback transformer, when I1 has current, I2 has no current.

I1=Bi*(L1/ur+L2)/(u0*N1) can be calculated.

Maximum input power of transformer P1=I1*V*T*D*0.5=0.5*Bi*(L1/ur+L2)/(u0*N1)*V*D. If power of transformer P0 is required, then maximum power of transformer P1

Fourth, reverse transformer (continuous)

Oscillogram of magnetic flux density versus time t

Select B=Br. V=N*Br*Ae/t1, find N, and round up N to an integer Ni as the number of winding turns.

After choosing Ni, Bi=V*t1/(Ni*Ae) can be obtained at this time.

Formula Pass 2:

Bi=u0*(N1*I1)/(L1/ur+L2).

Bmax=u0*(N1*Imax)/(L1/ur+L2).

In a flyback transformer, when I1 has current, I2 has no current.

I1=Bi*(L1/ur+L2)/(u0*N1) can be calculated. Imax=Bmax*(L1/ur+L2)/(u0*N1)

Maximum input power of transformer P1=(Imax-0.5*I1)*V*D=0.5*(Bmax-0.5Br)*(L1/ur+L2)/(u0*N1)*V *D. If power of transformer P0 is required, then maximum power of transformer P1

V. Conclusion

The flyback transformer can increase maximum output power of transformer by increasing air gap. The maximum power of a direct transformer is independent of air gap.

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