def ReferenceImpedance(S, Z0f, Z0i=None, Kf=None, Ki=None):
"""Changes the reference impedance and scaling factor
@param S s-parameter matrix to convert
@param Z0f the reference impedance to convert to
@param Z0i (optional) the reference impedance of the s-parameters (assumed 50 Ohms)
@param Kf (optional) assumed to be sqrt(Z0f)
@param Ki (optional) assumed to be sqrt(Z0i)
@return the converted s-parameters
@see Z0KHelper to see how the reference impedance
and scaling factor are determined."""
(Z0f, Kf) = Z0KHelper((Z0f, Kf), len(S))
(Z0i, Ki) = Z0KHelper((Z0i, Ki), len(S))
I = matrix(identity(len(S)))
p = (matrix(Z0f) - matrix(Z0i)) * (matrix(Z0f) + matrix(Z0i)).getI()
Kf = matrix(Ki) * matrix(Kf).getI()
S = matrix(S)
return (Kf * (I - p).getI() * (S - p) * (I - p * S).getI() * (I - p) *
Kf.getI()).tolist()
def ReferenceImpedance(S,Z0f,Z0i=None,Kf=None,Ki=None):
"""Changes the reference impedance and scaling factor
@param S s-parameter matrix to convert
@param Z0f the reference impedance to convert to
@param Z0i (optional) the reference impedance of the s-parameters (assumed 50 ohms)
@param Kf (optional) assumed to be sqrt(Z0f)
@param Ki (optional) assumed to be sqrt(Z0i)
@return the converted s-parameters
@see Z0KHelper to see how the reference impedance
and scaling factor are determined."""
(Z0f,Kf)=Z0KHelper((Z0f,Kf),len(S))
(Z0i,Ki)=Z0KHelper((Z0i,Ki),len(S))
I=array(identity(len(S)))
p=(array(Z0f)-array(Z0i)).dot(inv(array(Z0f)+array(Z0i)))
Kf=array(Ki).dot(inv(array(Kf)))
S=array(S)
return (Kf.dot(inv(I-p)).dot(S-p).dot(
inv(I-p.dot(S))).dot(I-p).dot(inv(Kf))).tolist()
def Z2S(Z, Z0=None, K=None):
"""Converts Z-parameters to s-parameters
@param Z list of list representing Z-parameter matrix to convert
@param Z0 (optional) float or complex or list of reference impedance (defaults to None).
@param K (optional) float or complex or list of scaling factor (defaults to None).
@see Z0KHelper to see how the reference impedance
and scaling factor are determined."""
(Z0, K) = Z0KHelper((Z0, K), len(Z))
Z = array(Z)
return (inv(K).dot(Z - Z0).dot(inv(Z + Z0)).dot(K)).tolist()
def S2Z(S, Z0=None, K=None):
"""Converts s-parameters to Z-parameters
@param S list of list representing s-parameter matrix to convert
@param Z0 (optional) float or complex or list of reference impedance (defaults to None).
@param K (optional) float or complex or list of scaling factor (defaults to None).
@see Z0KHelper to see how the reference impedance
and scaling factor are determined."""
(Z0, K) = Z0KHelper((Z0, K), len(S))
I = identity(len(S))
S = array(S)
return (K.dot(I + S).dot(inv(I - S)).dot(Z0).dot(inv(K))).tolist()
def S2Y(S,Z0=None,K=None):
"""Converts s-parameters to Y-parameters
@param S list of list representing s-parameter matrix to convert
@param Z0 (optional) float or complex or list of reference impedance (defaults to None).
@param K (optional) float or complex or list of scaling factor (defaults to None).
@see Z0KHelper to see how the reference impedance
and scaling factor are determined."""
(Z0,K)=Z0KHelper((Z0,K),len(S))
I=matrix(identity(len(S)))
S=matrix(S)
return (K*Z0.getI()*(I-S)*(I+S).getI()*K.getI()).tolist()
def Y2S(Y, Z0=None, K=None):
"""Converts Y-parameters to s-parameters
@param Y list of list representing Y-parameter matrix to convert
@param Z0 (optional) float or complex or list of reference impedance (defaults to None).
@param K (optional) float or complex or list of scaling factor (defaults to None).
@see Z0KHelper to see how the reference impedance
and scaling factor are determined."""
(Z0, K) = Z0KHelper((Z0, K), len(Y))
I = matrix(identity(len(Y)))
Y = matrix(Y)
return (K.getI() * (I + Z0 * Y).getI() * (I - Z0 * Y) * K).tolist()
def S2ABCD(S,Z0=None,K=None):
"""Converts s-parameters to ABCD parameters.
@param S list of list representing s-parameter matrix to convert
@param Z0 (optional) float or complex or list of reference impedance (defaults to None).
@param K (optional) float or complex or list of scaling factor (defaults to None).
@note
Supports only two-port devices.\n
@see Z0KHelper to see how the reference impedance
and scaling factor are determined."""
(Z0,K)=Z0KHelper((Z0,K),len(S))
Z01=Z0.item(0,0)
Z02=Z0.item(1,1)
K1=K.item(0,0)
K2=K.item(1,1)
C11=matrix([[0,K2],[0,K2/Z02]])
C12=matrix([[0,K2],[0,-K2/Z02]])
C21=matrix([[K1,0],[-K1/Z01,0]])
C22=matrix([[K1,0],[K1/Z01,0]])
return array((C21+C22*S)*((C11+C12*S).getI())).tolist()
def Sp2Sw(Sp,Z0w=None,Z0p=None,Kw=None):
"""Converts power-wave s-parameters to pseudo-wave s-parameters
@param Sp list of list power-wave based s-parameter matrix to convert
@param Z0w (optional) the reference impedance of the pseudo-wave based s-parameters (assumed 50 Ohms)
@param Z0p (optional) the reference impedance of the power-wave based s-parameters (assumed 50 Ohms)
@param Kw (optional) the scaling factor of the pseudo-wave based s-parameters (assumed to be sqrt(Z0w)
@return the converted s-parameters in pseudo-waves
@see Z0KHelper to see how the reference impedance
and scaling factor are determined for pseudo-waves.
@see Z0KHelperPW to see the reference impedance
and scaling factor are determined for power waves.
"""
if Z0p is None:
Z0p=Z0w
(Z0w,Kw)=Z0KHelper((Z0w,Kw),len(Sp))
(Z0p,Kp)=Z0KHelperPW(Z0p,len(Sp))
Sp=matrix(Sp)
Sw=(Kw.getI()*Kp*Z0p.real.getI()*((Z0p.conjugate()-Z0w)+(Z0p+Z0w)*Sp)*
((Z0p.conjugate()+Z0w)+(Z0p-Z0w)*Sp).getI()*Kw*Kp.getI()*Z0p.real)
return Sw
def Sp2Sw(Sp,Z0w=None,Z0p=None,Kw=None):
"""Converts power-wave s-parameters to pseudo-wave s-parameters
@param Sp list of list power-wave based s-parameter matrix to convert
@param Z0w (optional) the reference impedance of the pseudo-wave based s-parameters (assumed 50 ohms)
@param Z0p (optional) the reference impedance of the power-wave based s-parameters (assumed 50 ohms)
@param Kw (optional) the scaling factor of the pseudo-wave based s-parameters (assumed to be sqrt(Z0w)
@return the converted s-parameters in pseudo-waves
@see Z0KHelper to see how the reference impedance
and scaling factor are determined for pseudo-waves.
@see Z0KHelperPW to see the reference impedance
and scaling factor are determined for power waves.
"""
if Z0p is None:
Z0p=Z0w
(Z0w,Kw)=Z0KHelper((Z0w,Kw),len(Sp))
(Z0p,Kp)=Z0KHelperPW(Z0p,len(Sp))
Sp=array(Sp)
Sw=inv(Kw).dot(Kp).dot(inv(Z0p.real)).dot((Z0p.conj()-Z0w)+(Z0p+Z0w).dot(Sp)).dot(
inv((Z0p.conj()+Z0w)+(Z0p-Z0w).dot(Sp))).dot(Kw).dot(inv(Kp)).dot(Z0p.real)
return Sw.tolist()
def ABCD2S(ABCD, Z0=None, K=None):
"""Converts ABCD parameters to s-parameters.\n
@param ABCD list of list representing ABCD matrix to convert.
@param Z0 (optional) float or complex or list of reference impedance (defaults to None).
@param K (optional) float or complex or list of scaling factor (defaults to None).
@note
Supports only two-port devices.\n
@see Z0KHelper to see how the reference impedance
and scaling factor are determined.
"""
(Z0, K) = Z0KHelper((Z0, K), len(ABCD))
Z01 = Z0.item(0, 0)
Z02 = Z0.item(1, 1)
K1 = K.item(0, 0)
K2 = K.item(1, 1)
C11 = matrix([[0, 0], [1.0 / (2.0 * K2), Z02 / (2.0 * K2)]])
C12 = matrix([[1.0 / (2.0 * K1), -Z01 / (2.0 * K1)], [0, 0]])
C21 = matrix([[0, 0], [1.0 / (2.0 * K2), -Z02 / (2.0 * K2)]])
C22 = matrix([[1.0 / (2.0 * K1), Z01 / (2.0 * K1)], [0, 0]])
return array((C21 + C22 * ABCD) * ((C11 + C12 * ABCD).getI())).tolist()