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Nexxim Simulator >
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   Voltage-Controlled Current Source, LaPlace       

Voltage-Controlled Current Source, LaPlace

 

VCCS LaPlace Netlist Format

The voltage-controlled current source with LaPlace transfer function uses two different formats, the coefficient format and the pole zero format.

Coefficient Format

In the coefficient format, H(s) is specified by giving the coefficients of the transfer function polynomials:

Gxxxx out+ out- LAPLACE in+ in- a0[,] ... aN / b0[,] ...bD

[SCALE=val] [TC1=val] [TC2=val] [M=val]

out+ is the positive node and out- is the negative node of the current source. The entry LAPLACE selects the G element LaPlace transfer function type. in+ and in- are the positive and negative nodes for the control voltage. The division symbol (/) in the instance line is required syntax.

Note 

Comma separators between the a and b entries are optional. Spaces may be used as separators instead of commas.

The function of the device is expressed as:

I(out+, out-) = SCALE ´ H(s) ´ V(in+, in-)

The transfer function H(s) is the ratio of two polynomials in the complex variable s.

[spacer]

 

The coefficients (a0 ... aN) specify the numerator polynomial of the ratio. The coefficients (b0 ... bD) specify the denominator polynomial. The subscripts N and D represent the order of the numerator and denominator respectively. The first coefficients in both numerator and denominator (a0 and b0) are constants, which must be specified even if they are zero. Thus, leading zeros are significant. In addition, intermediate zero-valued coefficients must be explicitly supplied in order to have the non-zero coefficients applied to the correct powers of s. Trailing zeros are not significant, and are automatically removed.

For example, to specify the following transfer function (where coefficient a1=0):

[spacer]

 

A coefficient format netlist would contain the following statement:

Gex1 out gnd LAPLACE in gnd 1, 0, 2 / 1, 1, 3

 

Note 

The order of the numerator (N) may not exceed the order of the denominator (D), otherwise Nexxim will post an error message and disregard the device.

Pole Zero Format

The pole zero format specifies the complex roots of the transfer function polynomials:

Gxxxx out+ out- LAPLACE in+ in-
rz1 iz1 ... rzN izN / rp1 ip1 ... rpD ipD
POLE [SCALE=val] [TC1=val] [TC2=val] [M=val]

The pole zero syntax must include the keyword POLE. The slash (/) is required. The nodes and other parameters are the same as for the coefficient format.

The parameters rz1 iz1... rzN izN in the numerator are the complex zeros of the transfer function. The parameters rp1 ip1... rpD ipD in the denominator are the complex poles of the transfer function.

[spacer]

 

Both poles and zeros are complex numbers with a real part and an imaginary part. Each root must specify the magnitudes of both real and imaginary parts even if one of them is zero (j, the square root of -1, does not need to be entered). The list must also provide the complex conjugate of each root when the magnitude of the imaginary part is nonzero. The roots may be entered in any order.

For example, to specify zeros of s-1, s-2j with complex conjugate s-(-2j), s-(-1+3j) with complex conjugate s-(-1-3j), the denominator entry would be:

1 0 0 2 0 -2 -1 3 -1 -3

 


LaPlace VCCS Instance Parameters

Parameter

Description

Unit

Default

a0 ... aN

Coefficients of the numerator polynomial (coefficient syntax)

None

None

b0 ... bD

Coefficients of the denominator polynomial (coefficient syntax)

None

None

rz1 iz1 ... rzN izN

Complex zeros (pole/zero syntax)

None

None

rp1 ip1 ... rpD ipD

Complex poles (pole/zero syntax)

None

None

POLE

Selects pole/zero syntax

None

Coefficient syntax

M

Multiplier to simulate multiple elements

None

1.0

SCALE

Scale factor 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


VCCS LaPlace Element Netlist Examples

G21 21 0 LAPLACE 31 0 0.1 2.2 -.3 / 0.25 -2.1 0.33 -.4

G14 33 0 LAPLACE 44 0 .4 0 .35 -.2 .35 .2 / 1.0 2.5 1.0 -2.5
+ .56 0 1.8 0 POLE




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