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   Current-Controlled Current Source, Polynomial       

Current-Controlled Current Source, Polynomial

 

Polynomial CCCS Netlist Format

The format for a polynomial current-controlled current source (CCCS) is:

Fxxxx out+ out- [CCCS] POLY(N)

vin1 [vin2 [vin3]]

[MAX=val] [MIN=val] [SCALE=scale] [M=val]

[TC1=val] [TC2=val] [ABS=0|1]

p0 [p1 ... pK]

n+ is the positive node and n- is the negative node of the current source. The entry CCCS is the default for the F element type. The entry POLY is required to identify the polynomial CCCS type. The number of inputs, N, can be 1, 2, or 3. The controls are currents through voltage sources defined elsewhere in the netlist. If N is not specified, 1 is the default. vin1 through vin3 are the N sources for the control currents. p0 through pK are the K coefficients for the polynomial function. One coefficient must be provided.

 


Polynomial CCCS Instance Parameters

Parameter

Description

Unit

Default

ABS

1 = Output is an absolute value

None

0

M

Multiplier to simulate multiple elements

None

1.0

MAX

Maximum output current

Volt

None

MIN

Minimum output current

Volt

None

SCALE

Multiplier for current

None

1.0

TC1

Linear (1st-order) temperature coefficient

°K-1

0.0

TC2

Quadratic (2nd-order) temperature coefficient

°K-2

0.0


Polynomial CCCS Netlist Examples

F21 21 0 CCCS POLY(1) V1 1.1 2.1 0 3.1

F31 31 0 CCCS POLY(2) V1 V2 1.2 2.2 0 0 0 0 0 0 3.2 0

F41 41 0 CCCS POLY(3) V1 V2 V3 1.3 2.3 0 0

+ 0 0 0 0 0 0

+ 0 3.3 0 0 0 0 0 0 0 4.3

 

Notes

The functional equation for the polynomial CCCS is:

I(n+, n-) = polynomial ´ SCALE ´ (1 + DT ´ TC1 + DT2 ´ TC2)

If the result is less than MIN,

I(n+, n-) = MIN

If the result is greater than MAX,

I(n+, n-) = MAX

The polynomial depends on the number of inputs (N) and the number of polynomial coefficients (K). Each polynomial has terms of order (O), the sum of the exponents of the elements in the term. The list of coefficients must include coefficients for every term up to and including the complete group of terms with the highest order in the specified polynomial, using zero coefficients for any intermediate or trailing terms that are not to be computed.

When N=1, the polynomial formula has one term each of order O{0, 1, ... K}:

p0 + p1 ´ I(vin1) + ... pK ´ I(vin1)K

Each coefficient must be a real value or zero to represent a missing term. For example, to specify a CCCS between nodes 21 and 0 whose output, controlled by the current across voltage source V1, is described by the one-input polynomial 1.1 + 2.1 ´ I(V1) + 3.1 ´ I(V1)3, the instance statement would set coefficients p0=1.1, p1=2.1, p2=0, and p3=3.1:

F21 21 0 CCCS POLY(1) V1 1.1 2.1 0 3.1

(The control voltage source V1 would be defined on its own instance line elsewhere in the netlist.)

When N=2, the polynomial formula can have more than one term in each order grouping:

O(0)

p0 +

O(1)

p1 ´ I(vin1) +

p2 ´ I(vin2) +

O(2)

p3 ´ I(vin1)2 +

p4 ´ I(vin1) ´ I(vin2-) +

p5 ´ I(vin2)2 +

O(3)

p6 ´ I(vin1)3 +

p7 ´ I(vin1)2 ´ I(vin2) +

p8 ´ I(vin1) ´ I(vin2)2 +

p9 ´ I(vin2)3 +

O(4)

...

For example, to specify a CCCS between nodes 31 and 0 whose output, controlled by the currents across voltage sources V1 and V2, is described by the two-input polynomial 1.2 + 2.2 ´ I(V1) + 3.2 ´ I(V1) ´ I(V2)2, the instance statement would set coefficients p0=1.2, p1=22, and p8=3.2. Intermediate coefficients p2 through p7 and trailing coefficient p9 are set to 0:

F31 31 0 CCCS POLY(2) V1 V2 1.2 2.2 0 0 0 0 0 0 3.2 0

When N=3, the polynomial formula becomes:

O(0)

p0 +

O(1)

p1 ´ I(vin1) +

p2 ´ I(vin2) +

p3 ´ I(vin3) +

O(2)

p4 ´ I(vin1)2 +

p5 ´ I(vin1) ´ I(vin2) +

p6 ´ I(vin1) ´ I(vin3) +

p7 ´ I(vin2)2 +

p8 ´ I(vin2) ´ I(vin3) +

p9 ´ I(vin3)2 +

O(3)

p10 ´ I(vin1)3 +

p11 ´ I(vin1)2 ´ I(vin2) +

p12 ´ I(vin1)2 ´ I(vin3) +

p13 ´ I(vin1) ´ I(vin2)2 +

p14 ´ I(vin1) ´ I(vin2) ´ I(vin3) +

p15 ´ I(vin1) ´ I(vin3)2 +

p16 ´ I(vin2)3 +

p17 ´ I(vin2)2 ´ I(vin3) +

p18 ´ I(vin2) ´ I(vin3)2 +

p19 ´ I(vin3)3 +

O(4)

...

For example, to specify a CCCS between nodes 41 and 0 whose output, controlled by the currents across voltage sources V1, V2, and V3, is described by the three-input polynomial 1.3 + 2.3 ´ I(V1) + 3.3 ´ I(V1)2 ´ I(V2) + 4.3 ´ I(V3)3, the instance statement would set coefficients p0=1.3, p1=2.3, p11=3.3, and p19=4.3. Intermediate coefficients p2 through p10 and p12 through p18 are set to 0 (since p19 is the coefficient for the highest term with order 3, no trailing zeros are needed):

F41 41 0 CCCS POLY(3) V1 V2 V3 1.3 2.3 0 0

+ 0 0 0 0 0 0

+ 0 3.3 0 0 0 0 0 0 0 4.3

 




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