5.1.1 Transmission line port excitation

QuickWave offers matched modal excitation based on the field and impedance template. It is available for transmission line port, which is interchangeably called wave port or template port, marked as a source. The transmission line port describes a port defined by integrals of fields over a cross-section of an arbitrary transmission line. To excite the structure and extract any parameters at the Transmission line port we need to calculate a mode template, which is a set of transverse E and H fields of a particular mode considered for a particular frequency f in an infinite section of the transmission line (for more details refer to Template mode generation procedure).

For transmission line port excitations six excitation mode types are available:

· TEM - is typically used for exciting two-conductor TEM transmission lines. During the TEM template generation the unitary potential is assigned to the “first” conductor (indicated by the excitation point) and zero potential to all the other conductors. When the exciting field of the transmission line port is chosen to be TEM, the template becomes quasi-static template. For practical discussion refer to User Guide 3D: Planar circuit example, excited with TEM mode.

Note that TEM mode could also be applied to some cases of three-conductor lines. For example, for the most interesting (even) mode of a coplanar line we can assume two grounded surfaces and only one "hot" strip. However, the above procedure for TEM template generation cannot correctly generate the template for odd-mode in a coplanar line and in general other modes in multi-conductor transmission lines. In those cases we should use an advanced type of the quasi-static template called multiTEM.

multiTEM – this is quasi-static template mode, applicable to multi-conductor TEM lines. Unlike the TEM option, with multiTEM option the software does not try to locate geometrically the "first" conductor. In fact, it ignores the location of the excitation point in the port (indicating the “first” conductor for TEM option). Instead, multiTEM option allows defining TEM templates by assigning a specific quasi-static potential to each of the conductor. It assigns a particular potential based on the settings made for a particular metal material of which the conductor is made, in a particular port. Thus, if we want to create mode templates with N different potentials at N strips, we must declare at least N different metal materials. These metal materials of different names may have the same physical parameters (for example they may all be assumed to be perfect conductors) and differ only by port-potential settings. For practical discussion concerning the multiTEM option, refer to the User Guide 3D: Multi-conductor transmission lines example.
planeTEM - this is another option of the TEM family, designed for a specific case. When we consider a rectangular TEM port limited by two electric and two magnetic walls, the field distribution is constant in space. Thus we do not need to calculate it but can just assume the constant field distribution with a vertical (V) or horizontal (H) polarisation. We need to be careful when applying planeTEM excitation. It is up to the user to verify that the port obeys the above mentioned assumptions and that the polarisation is correctly chosen. Its application may save quite a lot of computing time when planeTEM assumptions are met and the port is large in terms of the number of FDTD cells. For practical discussion concerning planeTEM option, refer to User Guide 3D: Plane TEM example.
low-order modes in homogeneous rectangular waveguides – For automatic dynamic templates QuickWave can automatically introduce the mode parameters (most importantly effective permittivity) for QW-3D analysis for the following low-order rectangular waveguide modes: TE10, TE01, TE11, TM11. In calculation of the mode parameters the software assumes that the size of the port matches the size of the waveguide and that the waveguide is filled with air. If this is not true, the user should introduce the proper corrections to the set of parameters. The following formulas apply to calculating the effective permittivity value:

- rectangular waveguide filled with dielectric of e_r:

effective permittivity = ε_r {1-}

f_c – cut-off frequency of the mode

f – operating frequency

- rectangular waveguide filled with material of e_r and μ_r:

effective permittivity = ε_rμ_r {1-}

f_c – cut-off frequency of the mode

f – operating frequency

It is worth noting that for air-filled rectangular waveguide the effective permittivity automatically calculated by the software is:

- effective permittivity = 0 for any guide and any mode at cut-off frequency

- effective permittivity < 0 any guide and any mode below cut-off frequency

In simulation scenarios, where only half of the waveguide has been drawn/meshed (with respect to the m and n index) utilising the corresponding symmetries of the circuit, the symmetry option H or V, available in port settings dialogue, should be checked. This instructs the software to take double port dimension along m, n for calculating cutoff frequency, and thus effective permittivity, for the mn mode.

For a general mn mode, the index m is assumed to correspond to: x dimension for ports located in the XY-plane or XZ-plane; y dimension for the ports located in the YZ-plane.

low-order modes in homogeneous circular waveguides - for automatic dynamic templates QuickWave can automatically introduce the mode parameters (most importantly effective permittivity) for QW-3D analysis for the following low-order circular waveguide modes: TE11, TM01. In QW-V2D operation, this capability is restricted to the following circular waveguide modes: TMn1, TMn2, TEn1, TEn2, where n is angular variation defined for the project. In calculation of the mode parameters the software assumes that the size of the port matches the size of the waveguide and that the waveguide is filled with air. If this is not true, the user should introduce the proper corrections to the set of parameters. The following formulas apply to calculating the effective permittivity value:

- circular waveguide filled with dielectric of e_r:

effective permittivity = ε_r {1-}

f_c – cut-off frequency of the mode

f – operating frequency

- circular waveguide filled with material of e_r and μ_r:

effective permittivity = ε_rμ_r {1-}

f_c – cut-off frequency of the mode

f – operating frequency

It is worth noting that for air-filled circular waveguide the effective permittivity automatically calculated by the software is:

- effective permittivity = 0 for any guide and any mode at cut-off frequency

- effective permittivity < 0 any guide and any mode below cut-off frequency

For a general mn mode, the index m is assumed to correspond to: x dimension for ports located in the XY-plane or XZ-plane; y dimension for the ports located in the YZ-plane.

· low- and high- order analytical waveguide modes – for analytical dynamic templates a rectangular and circular waveguide mode of an arbitrary order can be generated. The user should set a required mode: Rect_TE, Rect_TM, Circ_TE or Circ_TM and values of mode indices m and n. Note that for Analytical mode the software assumes that the size of the port matches the size of the waveguide and the waveguide is filled with air.

For a general mn mode, the index m is assumed to correspond to: x dimension for ports located in the XY-plane or XZ-plane; y dimension for the ports located in the YZ-plane.

Arbitrary – this option is designated for arbitrary modes in arbitrarily shaped waveguides. It should be used for generating higher order modes in automatic dynamic templates, in case of inhomogeneously filled waveguides or quasi-TEM lines at high frequencies.

Let us stress that QW-3D is very flexible in terms of choice of the mode in arbitrarily shaped and inhomogeneous transmission lines forming the ports of the structure. The price for this flexibility is the need to set several parameters enabling the software to find the mode of interest. The following rules-of-thumb for setting effective permittivity may be useful:

- any guide, any mode at cut-off:

effective permittivity = 0

- empty rectangular or circular waveguide filled with air:

effective permittivity = {1-}

f_c – cut-off frequency of the mode

f – operating frequency

- rectangular or circular waveguide filled with dielectric of e_r:

effective permittivity = ε_r {1-}

f_c – cut-off frequency of the mode

f – operating frequency

- rectangular or circular waveguide filled with material of e_r and μ_r:

effective permittivity = ε_rμ_r {1-}

f_c – cut-off frequency of the mode

f – operating frequency

- inhomogeneous quasi-TEM line including dielectrics of e₁ < e₂ <..< e_n:

e₁ < effective permittivity < e_n

Transmission line port sources may be used for S-parameters extraction. To allow application of the differential method, they must be accompanied by reference planes (for details refer to S-parameters. The reference plane is the plane at which the data for S-parameters calculation is collected. If the port is not accompanied by reference plane, it will serve as source but it will be ignored from the point of view of S-matrix analysis. As default, the transmission line port source is accompanied by reference plane.

The user should place the reference plane in the proper position taking into account the following criteria:

- The port must be defined on a segment of a transmission line such that its geometry and material filling between the port plane and the reference plane, and three cells beyond the reference plane, do not change.

- The reference plane must not be closer than two cells from the port plane but for better accuracy it should rather be moved at least 4-5 cells towards the circuit.

- The S-parameters are calculated using the vector product of the simulated fields and the mode templates to filter out the influence of the modes other than the considered one. Nevertheless the presence of other modes may have some influence on the accuracy, especially when calculating wide-band characteristics of inhomogeneously filled lines. That is why it is recommended that thereference plane be kept at a safe distance from the discontinuities, which produce a high, content of unwanted modes.

- The position of the reference plane rectangle in the plane perpendicular to the direction of propagation should be exactly the same as of the corresponding port. If you move the reference plane graphically on the screen please observe that it is moved only in the direction perpendicular to the port plane.

Note that a reference plane defined in the Input Interface remains at its user-defined position only if this position coincides with FDTD cell edges (i.e., a plane where tangential E-fields are available in QW-Simulator). If not, the reference plane is shifted by the software to the nearest E-field plane for ports oriented along the Z-axis; or to the nearest E-field plane in the positive X- or Y-direction for ports oriented along the X- or Y-axis, respectively.

Each transmission line port can be defined as Source or Load. The declaration of the port as a source means that it will serve as the input port in the case of Sk1 element analysis, which uses excitation from one port only. To avoid confusion in the S-matrix interpretation it is recommended that this port be marked as port number one (Sk1 parameters are always extracted with respect to port number one, without checking whether this is really a source). In the case of Smn analysis each port included in S‑parameters extraction will serve as a source in one of the consecutive simulations.

Let us also note that it is possible to define in the same place two different ports operating on two different transmission line modes (like for example vertical and horizontal polarisation in a square waveguide). In this case we define in the same place two transmission line ports and assign to each of them different mode template by a proper choice of excitation parameters for template generation. Such a process has been exemplified in User Guide 3D: Septum polariser, User Guide 3D: First insight template generation - low-order waveguide modes, and User Guide 3D: Septum polariser as a six-port with higher-order waveguide modes.

Transmission line ports are modal matched ports. The matching is realised by introducing superabsorbing boundary conditions in the plane right behind the port. To assure high level of absorption, appropriate effective permittivity for absorbing boundary conditions needs to be assumed. QuickWave allows the user to manually define the permittivity effective for absorption or take advantage from Auto option, which assigns the value of effective permittivity calculated during the mode template generation process.