LineCalc is a utility that is a part of HPEESof, that allows you to calculate the dimensions of a uniform waveguide such as microstrip, coupled microstrip, strip line, or coplanar waveguide for a given impedance and substrate dimensions. It can also calculate the characteristic line impedance of the fundamental mode given the specific dimensions of the waveguide. The procedure below provides first a basic working of LineCalc, and then some examples of using LineCalc for uniform waveguide analysis. It must be emphasized at this point that LineCalc performs approximate calculations for the waveguide parameters based on well developed empirical formulas. In general, the accuracy should be < 1 % for most calculations. However, in most cases, the results are not exact.

1. Logon to alpha or beta in the EWL. If you login remotely, make sure to set up your TERM and DISPLAY environment variables in order to open an X-window on your remote terminal. If you are logging in from within the EWL, this will be defaulted.
2. Move to your hpads working directory
3. From the UNIX prompt, type: source /usr/local/env/csh.eesof
4. This previous step sets up the necessary environment variables to run LineCalc. Next, from the UNIX prompt, type: linecalc This will open a LineCalc window that should look appear as:



5. LineCalc performs computations for a number of waveguide types. The default type when it first comes up is a bilateral finline. To change the element type to something different, say microstrip, then with the mouse select the "Select…" button near the upper center of the window to the right of where it says "Element Type:". A window will pop up with a number of element types. Of most interest to us will be "MLIN" for a uniform microstrip line, "MCLIN" for uniform coupled microstrips, "SLIN" for a uniform strip line, "SCLIN" for uniform coupled striplines, "CPW" for uniform coplanar waveguides, and "CPWG" for uniform conductor backed coplanar waveguides.

1. The presentation of the uniform microstrip line will be presented through an example. Assume that you want to design both 50 ohm and 70.71 ohm microstrip lines printed on a 10 mil Alumina substrate with an electrical length of 90 degrees at 5 GHz. Then perform the following steps:
2. Within the LineCalc window select MLIN for the element type.
3. Next, select the "Modify Substrate…" button. A window will pop up allowing you to set the substrate parameters. Set the relative permittivity (ER) to 9.8 (for Alumina), the substrate thickness (H) to 10 mils (the default units are in mils), the metalization thickness (T) to 0.150 mils (note: this will be the thickness of the microstrip line). RHO is the resistivity relative to gold. Leaving RHO = 1.0 declares that the conductors are gold. If RHO > 1, then the conductor has a resistivity > gold (which implies a lower conductivity), and visa versa for the case when RHO < 1. Given that Gold has a conductivity of 4.1e7 (or a resistivity of 1/(4.1e7)), and you want to assume a Copper line (which has a conductivity of 5.8e7). Then you would set RHO = 4.1e7/5.8e7 = 0.7069. For the purposes of this example, leave RHO = 1. The window will appear as below. Then click on "Apply", then "OK" to finish.

 



4. Given this substrate, let us use LineCalc to determine the strip width for a 50 ohm line, then a 70.71 ohm line. Also, we want to determine the physical line length of a quarter wave length line at 5 GHz. To proceed, in the main LineCalc window, change the frequency to 5 GHz. Next, set Zo to 50 ohms (the default unit), and the electrical length E_EFF to 90 degrees (the default unit). Note that E_EFF = beta times length. Assuming beta = 2*Pi/lambda, then when length = lambda/4, then E_EFF = Pi/2, or 90 degrees. Next, we will let LineCalc calculate W and L, the strip width and the length. To this end, click the mouse button on the up arrow on the center right side of the window. This implies that given Zo and E_EFF, LineCalc will compute W and L. The down arrow would do the opposite. Namely, given W and L, compute Zo and E_EFF.
5. After clicking on the up arrow, wait a few seconds as LineCalc performs the calculation. When it is done, you will notice the values for W and L changing. The window should appear as:

1. As a second example, select the element type as MCLIN for coupled microstrip lines.
2. Modify the substrate again for a 10 mil thick (H = 10) Alumina substrate (ER = 9.8). Also, set the metallization thickness to 0.15 mils and the resistivity to that of Gold (RHO = 1.0).
3. In the main LineCalc window, set the frequency to 18 GHz (X-band).
4. Next, assume that we want to design a coupled line with –20 dB of coupling and matched to a 50 ohm line impedance. For –20 dB of coupling, we find that C = 0.1. Also, given C, and Zo = 50 ohms, we find that Zoe = 55.277 ohms, and Zoo = 45.227 ohms. Thus, in the LineCalc window, set ZE = 55.277 ohms, and ZO = 45.227 ohms. Note that C_dB and Zo will automatically be set to –20 dB and 50 ohms, respectively. (You could have also done the reverse process, but at this point we need to know how to compute Zoe and Zoo!). Next, set E_MEAN = 90 degrees. This is the mean phase shift along the line. Note that it is a mean length since the even and odd modes have different propagation velocities, and hence different effective dielectric constants. Next, click on the up arrow to calculate the dimensions. You determine that W = 9.29 mils (the width of the two parallel microstrip lines), and S = 14.365 mils (the separation distance between the two lines). The length of the line for a 90 degree phase shift is 63.515 mils. This translates to an effective dielectric constant of 6.6705.
5. Repeat the same example for a –3 dB coupling coefficient. To this end, we find that Zoe = 120.913 ohms, Zoo = 20.675 ohms (for Zo = 50 ohms), and W = 2.974 mils, S = 0.193 mils, and L = 72.015 mils. Note that for stronger coupling, the separation must be extremely small (S = 0.193 mils x 0.0254 mm / mil = 0.0049 mm, or 4.9 microns!). While, this dimension is possible, it is near the tolerance limit for many fabrication processes. Also note that W must be much smaller to support such a high even mode line impedance.