Equivalent Circuit Construction for Common Mode Choke Coils (Theory)

When constructing equivalent circuits for common mode choke coils, the numerical value of the equivalent circuit is calculated mainly by performing measurements in three steps (STEPs 1 to 3).

	STEP1 Primary coil Impedance measurement (Primary and secondary coil input/output connections) *Obtain iron loss resistance, winding capacity	STEP2 Primary coil Impedance measurement (Secondary side coil SHORT) *Obtain Leakage inductance	STEP3 Primary coil DC resistance measurement (Secondary coil OPEN) *Obtain winding resistance
Measurement circuit
Parameters derived from measurements (STEP1) Co, Ro, and Lo are obtained using the impedance phase θ as a guide. Co: θ<-80deg Lo: θ>+80deg For Ro, use the resistance value at frequency fo below as a guideline.	Measure inductance Lo, including leakage inductance, resistance Ro corresponding to iron loss, and winding stray capacitance Co. Ro and Co are the total values of the primary and secondary coils. Lo is the sum of the magnetic fluxes generated by both the primary and secondary coils. While the inductance seems to be doubled, the primary and secondary coils are connected in parallel, so the result remains Lo.	Measure the leakage inductance Ls included in Lo obtained in STEP1. Due to magnetic coupling, Ls is the sum of the leakage inductances of the primary and secondary coils. When the secondary coil shorts, from the perspective of the primary coil, the magnetically coupled Lo is shorted and the residual leakage inductance Ls can be measured.	Measure D.C.R. DCRo of copper wire. Since the primary and secondary coils have the same number of winds, the measured value also applies to the secondary coil.
Separating measurement results into primary and secondary coils	C: Stray capacitance of winding for one circuit R: Iron loss equivalent resistance for one circuit Lo: Inductance for one circuit (including leakage inductance)	Lℓeak: Leakage inductance for one circuit 【note】Remarks About Lo‘ Lo minus Lℓeak is the inductance that acts on common mode noise.	DCR: D.C.R. for one terminal
Development to equivalent circuit considering magnetic coupling	Coupling coefficient k and mutual inductance M are calculated from Lo and Lℓeak obtained in STEPs 1 and 2, and the magnetic coupling of common mode choke coils can be reproduced by replacing the coil part with a T-type equivalent circuit. (Figure 1.) However, the following problems occur in the equivalent circuit of Figure 1. [Details of the problem] Mutual inductance M expresses magnetic coupling, meaning the electrical insulation of the primary and secondary coils cannot be reproduced. As a countermeasure, with SPICE and other simulations, if the coupling coefficient k is set to 1 or less, it is possible to perform simulations that incorporate the effects of leakage inductance. As such, we propose the equivalent circuit in Figure 2 as a method of reducing the number of elements and ensuring magnetic and electrical conformity.
Final equivalent circuit including D.C.R. and simulation error countermeasures	The final equivalent circuit shown on the left is completed by STEPs 1 to 3. Stray capacitance(C) Iron loss(R) Leakage inductance (Lℓeak) by coupling coefficient (k) These factors cause the high-frequency characteristics to deviate from the ideal characteristics. As such, this becomes a critical parameter when creating an equivalence circuit model for use in SPICE, etc.