Note that the default reference impedance of the Complex Impedance is zero and must always stay zero to function properly. In order to have a fixed impedance element, define the same Real(z11) and Imag(z11) values for the minimum and maximum frequencies of your circuit. Due to the interpolation between these two values, you will always get the same impedance value at all the frequencies in between those two limits.
== Transmission Lines ==
The standard SPICE provides two types of general-purpose transmission line models: lossless (TRA) and lossy (LTRA). These models are primarily intended for transient analysis. The lossless transmission line model is characterized by either its delay in seconds or by its normalized length at a given frequency. On the other hand, the lossy transmission line model is characterized by distributed RLCG [[parameters]]: resistance per unit length (R), inductance per unit length (L), capacitance per unit length (C), and conductance per unit length (G). Both [[B2.Spice A/D]] and [[RF.Spice]] offer the native SPICE transmission line models TRA and LTRA as passive devices.
However, [[RF.Spice]] also offers a number of other transmission line models specifically intended for use in RF circuit analysis. These include the generic T-Line, the generic coupled T-lines, and a variety of physical transmission line models.
==Generic T-Line==
[[File:tline.png|thumb|250px| The schematic symbol of the Generic T-Line device.]]
[[RF.Spice]] offers a passive device called Generic T-line with the keyboard shortcut “T”, which is a general purpose frequency-domain transmission line segment model. It is based on the native SPICE LTRA model, but with the following [[parameters]]:
* Z0: Characteristic Impedance in Ohms
* eeff: Effective Permittivity
* alpha: Attenuation Constant in dB/m
* len: Physical Length in meters
The default [[parameters]] of the Generic T-Line are Z0 = 50 Ohms, eeff = 1, alpha = 0, and len = 10mm. A unit effective permittivity implies a TEM transmission line because √ε<sub>eff</sub> = β / k<sub>0</sub>, where β is the propagation constant of the transmission line and k<sub>0</sub> = 2πf/c is the free space propagation constant, with f being the frequency in Hertz and c = 3e8 m/s being the speed of light. A zero attenuation constant represents a lossless transmission line. The Generic T-Line device is indeed a two-port network with a 2×2 scattering matrix or four S-parameters: s11, s21, s12 and s22. Obviously, this is a reciprocal and symmetric network, i.e., s11 = s22, and s21 = s12.
Note that N-port networks in [[RF.Spice]] have schematic symbols with 2N pins. Each pair of pins represents a port. In a similar way, the generic T-line has two ports and four pins. The pins are marked with plus and minus signs. For example, in the figure above, the pins P1+ and P1- together form Port 1. Normally, the negative pins are grounded, and the positive pins are connected to the other parts of the circuit.
{{Note | Proper grounding of the [[Transmission Lines|transmission lines]] device is critical for a successful simulation.}}
[[File:tline2.png|thumb|350px| The schematic symbols of the Generic Open Stub (left) and Generic Short Stub (right) devices.]]
==Open and Short Stubs==
The Generic Open Stub and Generic Short Stub are two one-port devices based on the Generic T-Line device. They represent terminated generic transmission line segments. In the open stub case, the termination load is Z<sub>L</sub> → ∞, and in the short stub case, the termination load is Z<sub>L</sub> = 0. The [[parameters]] of both open and short stub devices are the same as those of the generic T-line device.
[[File:tline3.png|thumb|250px| The schematic symbol of the Generic Coupled T-Lines device.]]
==Generic Coupled T-Lines==
Many passive RF devices such as directional couplers, hybrids and some filter designs involve segments of parallel coupled [[Transmission Lines|transmission lines]]. According to the coupled mode theory, one can define even and odd mode impedances for such [[Transmission Lines|transmission lines]]. The resulting RF structure can be modeled as a four-port network device as shown in the opposite figure. Note that the four-port device has eight pins. Ports 1 and 2 correspond to the input and output of the first transmission line segment, while Ports 3 and 4 correspond to the input and output of the second (coupled) line segment. It is very important to connect and ground the negative pins at the input and output of the two transmission line segments.
The Generic Coupled T-Lines device has the following [[parameters]]:
* Z0e: Even Mode Characteristic Impedance in Ohms
* Z0o: Odd Mode Characteristic Impedance in Ohms
* eeff: Effective Permittivity
* len: Physical Length in meters
This model assumes lossless [[Transmission Lines|transmission lines]].
[[File:tline4.png|thumb|450px| The schematic symbols of the Generic T-Line Discontinuity devices: (a) Open End, (b) Bend, (c) Step Junction, (d) Tee Junction and (e) Cross Junction.]]
==Generic T-Line Discontinuities==
In real practical RF circuits, you often need to transition from one transmission line to another or connect two or more [[Transmission Lines|transmission lines]] together. These transitions can be modeled as [[Multiport Networks|multiport networks]]. [[RF.Spice]] currently offers five generic T-Line discontinuity devices as follows:
* Generic Open End (a one-port)
* Generic Bend (a two-port)
* Generic Step Junction (a two-port)
* Generic Tee Junction (a three-port)
* Generic Cross Junction (a four-port)
The schematic symbols of these devices are shown in the opposite figure. Similar to other RF devices or [[Multiport Networks|multiport networks]], the negative pins of the ports must always be grounded. Unlike the T-line device described earlier which have models based on or derived from the standard SPICE LTRA, the generic T-line discontinuities have S-parameter-based models.
When you first place these discontinuity parts on your circuit, they have default S-parameter values. The default values have been chosen to be very general and may not necessarily represent the physics of your specific circuit. You must enter your own S-parameter values over the desired frequency range and replace the default values. These data can easily be generated in and imported from an electromagnetic simulation suite like [[EM.Cube]]. Unlike physical [[Transmission Lines|transmission lines]] like microstrip or coaxial line (to be discussed later) that have particular geometries and physical structures, the Generic T-Line device and Generic T-Line Discontinuities are very general by definition and do not have physical, material or dimensional [[parameters]]. You can model and simulate very complicated transmission line structures as well as open end, bend, step, tee or cross junctions based on those structures using [[EM.Cube]] and then import their S-parameter data into the corresponding discontinuity parts.
For more information about generic transmission line discontinuity devices, please refer to [[Glossary_of_Generic_RF_Devices | Glossary of Generic RF Devices]].
==Physical Transmission Line Types==
In addition to the Generic T-Line, [[RF.Spice]] also offers a number of physical [[Transmission Lines|transmission lines]] as follows:
* Microstrip Line
* Coupled Microstrips
* Covered Microstrip
* Suspended Microstrip
* Inverted Microstrip
* Coplanar Strips (CPS)
* Stripline
* Coupled Striplines
* Off-Center Stripline
* Coplanar Waveguide (CPW) Line
* Finite-Ground CPW Line
* Conductor-Backed CPW Line
* Coaxial Line
*Covered CPW
*Covered Conductor-Backed CPW
* CPW with a Superstrate
* Double-Layer CPW
* Twin-Lead Line
* Twisted-Pair Line
The physical transmission line types are characterized by their physical dimensions and material properties. The following table shows the [[parameters]] of each transmission line type:
{| class="wikitable"
|-
! Line Type !! Model Name !! [[Parameters]] !! Image !! Schematic Symbol
|-
| Microstrip Line || microstrip-line || len: line segment length in mm <br /> w: microstrip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity <br /> sigma: microstrip conductivity in S/m <br /> tand: substrate dielectric loss tangent <br /> t: metallization thickness in mm || [[File:microstrip.png]] || [[File:microstrip1.png|120px]]
|-
| Coupled Microstrips || coupled-microstrips || len: line segment length in mm <br /> w: strip width in mm <br /> s: microstrip spacing in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity || [[File:coupled_microstrips.png]] || [[File:coupled_microstrips1.png|120px]]
|-
| Covered Microstrip Line || microstrip-covered || len: line segment length in mm <br /> w: microstrip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity <br /> hc: cover height in mm || [[File:microstrip_cover.png]] || [[File:CoveredMS1.png|120px]]
|-
| Suspended Microstrip Line || microstrip-suspended || len: line segment length in mm <br /> w: microstrip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity <br /> b: height of substrate above ground in mm || [[File:SUSPMS.png]] || [[File:SuspMS1.png|120px]]
|-
| Inverted Microstrip Line || microstrip-inverted || len: line segment length in mm <br /> w: microstrip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity <br /> b: microstrip height above ground in mm || [[File:INVMS.png]] || [[File:InvMS1.png|120px]]
|-
| Coplanar Strips (CPS) Line || cps-line || len: line segment length in mm <br /> w: strip width in mm <br /> s: strip spacing in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity || [[File:CPS.png]] || [[File:CPS1.png|120px]]
|-
| Stripline || stripline || len: line segment length in mm <br /> w: strip width in mm <br /> b: parallel plate spacing in mm <br /> er: substrate relative permittivity <br /> sigma: strip conductivity in S/m <br /> tand: substrate dielectric loss tangent <br /> t: strip thickness in mm || [[File:stripline.png]] || [[File:stripline1.png|120px]]
|-
| Coupled Striplines || coupled-striplines || len: line segment length in mm <br /> w: strip width in mm <br /> s: strip spacing in mm <br /> b: parallel plate spacing in mm <br /> er: substrate relative permittivity || [[File:coupled_striplines.png]] || [[File:coupled_striplines1.png|120px]]
|-
| Off-Center Stripline || coupled-striplines || len: line segment length in mm <br /> w: strip width in mm <br /> s: offset from centerline in mm <br /> t: strip thickness in mm <br /> b: parallel plate spacing in mm <br /> er: substrate relative permittivity || [[File:OffCenter.png]] || [[File:OffStrp1.png|120px]]
|-
| Coplanar Waveguide Line || cpw-line || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity || [[File:cpw.png]] || [[File:cpw1.png|120px]]
|-
| Conductor-Backed CPW Line || cbcpw-line || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity || [[File:cbcpw.png]] || [[File:cbcpw1.png|120px]]
|-
| Covered CPW Line || cpw-covered || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> h: substrate thickness in mm <br /> hc: cover height in mm <br /> er: substrate relative permittivity || [[File:cpw_cover.png]] || [[File:CovCPW1.png|120px]]
|-
| Covered Conductor-Backed CPW Line || cbcpw-covered || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> h: substrate thickness in mm <br /> hc: cover height in mm <br /> er: substrate relative permittivity || [[File:cbcpw_cover.png]] || [[File:CovCBCPW1.png|120px]]
|-
| Finite-Ground CPW Line || fgcpw-line || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> g: ground strip width <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity || [[File:fgcpw.png]] || [[File:fgcpw1.png|120px]]
|-
| CPW Line with a Superstrate || cpw-super || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> g: ground strip width in mm <br /> h: substrate thickness in mm <br /> er: substrate relative permittivity <br /> hs: superstrate height in mm <br /> ers: superstrate relative permittivity || [[File:SuperCPW.png]] || [[File:SuperCPW1.png|120px]]
|-
| Double-Layer CPW Line || cpw-doublelayer || len: line segment length in mm <br /> w: slot width in mm <br /> s: center strip width in mm <br /> h1: lower substrate layer thickness in mm <br /> er1: lower substrate layer relative permittivity <br /> h2: upper substrate layer thickness in mm <br /> er2: upper substrate layer relative permittivity || [[File:DoubleCPW.png]] || [[File:DoubleCPW1.png|120px]]
|-
| Coaxial Line || coaxial-line || len: line segment length in mm <br /> r_in: inner conductor radius in mm <br /> r_out: outer conductor radius in mm <br /> er: dielectric core relative permittivity <br /> sigma: metal conductivity in S/m <br /> tand: dielectric core loss tangent || [[File:coax.png]] || [[File:coax1.png|120px]]
|-
| Twin-Lead Line || twin-lead || len: line segment length in mm <br /> r: wire radius in mm <br /> s: wire spacing in mm <br /> er: dielectric medium relative permittivity <br /> sigma: wire conductivity in S/m <br /> tand: dielectric medium loss tangent || [[File:twin.png]] || [[File:twin1.png|120px]]
|-
| Twisted-Pair Line || twisted-pair || len: line segment length in mm <br /> r: wire radius in mm <br /> s: wire spacing in mm <br /> T: number of twists per length in 1/m <br /> erc: dielectric cover relative permittivity <br /> erm: dielectric medium relative permittivity <br /> sigma: wire conductivity in S/m <br /> tand: dielectric cover loss tangent || [[File:twisted.png]] || [[File:twisted1.png|120px]]
|-
|}
[[File:tline5.png|thumb|450px| The schematic symbols of the some Physical Transmission Line Discontinuity devices. (Top Row) microstrip components: right-angled bend, mitered bend, tee and cross junctions, (Bottom Row) CPW components: open end, short end, gap and step junction.]]
==Physical Transmission Line Discontinuities==
Besides the Generic T-Line Discontinuity devices described earlier, [[RF.Spice]] also offers a large number of physical transmission line discontinuity devices based on some of the transmission line types listed above. Among these, the microstrip components are more widely used and have more variety. Unlike the generic T-line components which require that you supply the S-parameter data, the physical components are parameterized based on their geometrical and material properties. As a result, you simply enter the physical dimensions and other [[parameters]] and their S-[[parameters]] are automatically calculated by [[RF.Spice]] during the circuit simulation. In other words, the property dialog of these components contains their physical [[parameters]] only and does not show the values of their S-[[parameters]] as a function of frequency.
For more information about physical transmission line discontinuity devices, please refer to [[Glossary_of_Physical_Transmission_Lines_and_Components|Glossary of Physical Transmission Lines and Components]].
<p> </p>