## Mutually Coupled Coils: N Inductors (Closed Form): MUCN

### Symbol ### Parameters

Name Description Unit Type Default
ID Element ID Text M1
N Number of coils   2
L Self-inductance of coils(vector of N size) Inductance 1 nH
R Resistance of coils(vector of N size) Resistance 0 ohm
K1toN Coupling coefficient between coil #1 and coils #2 to #N (vector of N-1 size)   0
K2toN Coupling coefficient between coil #2 and coils #3 to #N (vector of N-2 size)   0
KN-1toN Coupling coefficient between coil #N-1 and coil #N (vector of 1 size)   0

### Parameter Details

K1toN, K2toN...KN-1toN. These dynamic vector parameters contain user-defined coupling coefficients between coils. The number of these parameters is N-1. Vector KitoN contains coupling coefficients between coil #i and coils from #i+1 to #N. The size of these vectors decreases as i increases. For example, if N=5 then KitoN vectors contain coupling coefficients K_ij:

K1toN = {K_12, K_13, K_14, K_1_5}

K2toN = {K_23, K_24, K_25}

K3toN = {K_34, K_35}

K4toN = {K_45}

MUCN checks the actual size of each vector and displays an error message if the actual size differs from what is expected.

### Parameter Restrictions and Recommendations

1. Number of coils N must comply with restriction: 2≤N≤100.

2. Coil inductance must be positive: Li >0, i=1…N

3. Coil resistance must be non-negative: Ri ≥0, i=1...N

4. Coupling coefficient between coils #i and #j must comply with restriction: -1≤K_ij≤1

### Implementation Details

Pin numbers for each coil are assigned by the convention i = coupled port and N+i= output port for each coil, N = number of coils. For example for coil 1, 1 is the coupled port and N+1 is the output port. Vci is the voltage across coil #i, i=1…N: where  ### Layout

This element does not have an assigned layout cell. You can assign artwork cells to any element. See “Assigning Artwork Cells to Layout of Schematic Elements” for details.