**5. Conclusion**

314 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

generator microwaves composed of the following elements (Fig.1):

while the last ones represent current patterns.

resistance ܴ ൌ ઢ

where we represented the tube microwave by the equivalent diagram deduced from its electric characteristic [2]-[3]-[6] which is formally similar to that of a diode of dynamic

validate this new model by carrying out tests that have been set up previously [2] on

 A high voltage transformer with magnetic shunt ratings: f=50 Hz, S=1650 VA, U1=220 V, and, no-load U2=2330 V (r'1 =100 Ω and r2=65 Ω, for n1=224 and n2=2400 turns). A cell composed of a condenser, its capacity C=0,9 µF and a diode high voltage DHV. A magnetron designed to operate under an approximate voltage of 4000 V. To obtain its nominal power, it needs an average current Imoy=300 mA, but without exceeding the peak current which might destroy it (Imax<1,2 A). The experimental curves are presented in Fig.6. The first three curves represent the shapes of voltage quantities

**Figure 7.** Experimental forms curves of the voltages and currents waves (nominal operating)

ઢ neighbor of 350 Ohms and threshold voltage E of about 3800 Volts. We

From the Simulink block modelling a non-linear inductance by introducing point by point its values, we performed a new model in two steps:

**Step 1.** A program M-file was developed and gives us the final results of the B-H curve fitting.

**Step 2.** By performing a function 'MATLAB Function' that replace us the nonlinear inductance of the current passing through this inductance as shown in Fig.4.

This approach can solve many problems of modeling, simulation and optimization of the electrical networks and electric machines also [7].

Thus, an improved procedure for modeling the nonlinear characteristic B-H of the ferromagnetic materiel (SF19) of this special transformer supplying one magnetron has been presented. Starting with a discrete set of measurement data of B and H, we have obtained two analytic expressions of B-H curve in terms of non-integer power series for the linear part of this curve and polynomial representation for the saturation region. Then, these expressions have been used for improving the old modelling of nonlinear inductances into the new one based on the determination of analytic expressions of each inductance. We validate the new π model (with three nonlinear inductances) of the transformer with magnetic shunts, used in HV supply for magnetron by MATLAB-SIMULINK code in nominal mode. A comparison between the numerical results and experimental ones has shown a significant agreement.
