Chien-Min, As far as I know, S-parameter is a port concept. So it creates confusion if you try to think it as a node concept. However, you can generate S-parameters using the .net statement for a circuit node, but the generated S-parameters are essentially the same for the two cases you described. Physically speaking they are different, but from .net statement point of view, they are equivalent. As for the S-parameter relations for the cascade networks, I can't find a simple relation. There is a straight-forward relation of ABCD matrix for cascaded networks, and the transform between S-parameter and ABCD matrix. But is there a simple relation formula to give out cascaded network's S-parameter, based on each subnetwork's S-parameter? Yu == Chien-Min Lin wrote: > >Appreciate very much for the subtle comment of Ross. >Now, it did work as expected in the analytical one. >To extend the study in S-parameters, the .sp script >is provided for a typical transmission line network >with some stubs: > > IN---[Tx1]---n1---[Tx2]---n2---[Tx3]---n3---[Tx4]---OUT > | | | | | > | | | | [Rd] >[Vin] [Sb1] [Sb2] [Sb3] | > | | | | 0 > 0 0 0 0 > > >(00) S-Parameters / .NET >********************************************************************* >.OPTION Post > + DCSTEP=1 >*--[ Transmission Line (W element): XFX ]---------------------------* > >.subckt nom_W4x1 1 2 3 4 Len_in=10 > $: Er=4.0 Zo =49.89 TD =2.03 num_sig=1 h1=4.65347 h2=4.9505 w=4 > W1 1 2 3 4 Umodel=umod N=1 L=Len_in >.model umod U Level=3 NL=1 Elev=2 Llev=0 Plev=1 Nlay=2 > + L11=8.453n > + > + Cr1=3.397p > + > + R1c=0.252 > + > + Gr1=0 > + > + R1s=2.90989e-05 >.ends nom_W4x1 > >*--[ Two-Port Network: Tx + Stub ]----------------------------------* >* >* IN---[Tx1]---n1---[Tx2]---n2---[Tx3]---n3---[Tx4]---OUT >* | | | | | >* | | | | [Rd] >* [Vin] [Sb1] [Sb2] [Sb3] | >* | | | | 0 >* 0 0 0 0 >*-------------------------------------------------------------------* > > Vin IN 0 AC 1.0 $: exciation > > X_Tx1 IN 0 n1 0 nom_W4x1 Len_in=1.0 $: unit = inch > X_Tx2 n1 0 n2 0 nom_W4x1 Len_in=1.0 > X_Tx3 n2 0 n3 0 nom_W4x1 Len_in=1.0 > X_Tx4 n3 0 OUT 0 nom_W4x1 Len_in=1.0 > > X_Sb1 n1 0 0 0 nom_W4x1 Len_in=0.2 > X_Sb2 n2 0 0 0 nom_W4x1 Len_in=0.2 > X_Sb3 n3 0 0 0 nom_W4x1 Len_in=0.2 > > Rd OUT 0 1E14 $: open load > >*-------------------------------------------------------------------* >.AC dec 500 1 8500Meg > >.NET V(OUT) Vin Rout=50.0 Rin=50.0 > >.probe AC S11 S11(dB) (-50,10) S11(p) (-180, 180) >.probe AC S21 S21(dB) (-50,10) S21(p) (-180, 180) >*-------------------------------------------------------------------* >.END >********************************************************************* > > >In brief, the S11 and S21 are referred to > _________ > V1+ | | V2+ > --> | 2-Port | <-- > Vin o-------+ +-------o Vout > <-- | Network | --> > V1- |_________| V2- > >that is, > S11 = V1-/V1+ while V2+ = 0 > S21 = V2+/V1+ while V2+ = 0 > >Nonetheless, is there well defined for S11_ni and S21_ni >as depicted in the branched network? > > IN---[Tx1]---n1---[Tx2]---n2---[Tx3]---n3---[Tx4]---OUT > | | | | | > | | | | [Rd] >[Vin] [Sb1] [Sb2] [Sb3] | > | | | | 0 > 0 0 0 0 > >That is, at Node n1: S11=? S21=? > n2: S11=? S21=? > n3: S11=? S21=? > >Can the .NET statements be applied in the .alt statements: > >.alt (01) .NET V(n1) Vin Rout=50.0 Rin=50.0 > .NET V(n1) Vin Rout=50.0 Rin=50.0 > .probe AC S11 S21 $: node n1 > >.alt (02) .NET V(n2) Vin Rout=50.0 Rin=50.0 > .NET V(n2) Vin Rout=50.0 Rin=50.0 > .probe AC S11 S21 $: node n2 > >.alt (03) .NET V(n3) Vin Rout=50.0 Rin=50.0 > .NET V(n3) Vin Rout=50.0 Rin=50.0 > .probe AC S11 S21 $: node n3 > > >However, it confuses me with my understanding in the 2-port >network. For instance, at the node n2: > > IN---[Tx1]---n1---[Tx2]---n2---[Tx3]---n3---[Tx4]---OUT > | | | | | > | | | +----> | [Rd] >[Vin] [Sb1] [Sb2] | [Sb3] | > | | | | | 0 > 0 0 0 | 0 > | > | > at n2: look into an open end > >is it needed to break/remove [Tx3... to the right of n2] by >terminating at 500000ohms: > > IN---[Tx1]---n1---[Tx2]---n2---+[50000ohms] > | | | > | | | >[Vin] [Sb1] [Sb2] > | | | > 0 0 0 > >such that > .NET V(n2) Vin Rout=50.0 Rin=50.0 > >can be applied to calculate S11 and S21 at n2? > >What is the difference in physics between these two models: >without removing [Tx3...] and 50000ohms terminated at n2? > >Thanks for all your sophisticated advice, indeed. > > >_________________________________________________________________ >Chat with friends online, try MSN Messenger: http://messenger.msn.com > >------------------------------------------------------------------ >To unsubscribe from si-list: >si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field > >or to administer your membership from a web page, go to: >//www.freelists.org/webpage/si-list > >For help: >si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field > >List archives are viewable at: > //www.freelists.org/archives/si-list >or at our remote archives: > http://groups.yahoo.com/group/si-list/messages >Old (prior to June 6, 2001) list archives are viewable at: > http://www.qsl.net/wb6tpu > > ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu