eee161 applied electromagnetics laboratory 3

Dr. Milica Markovic Applied Electromagnetics page 1

EEE161 Applied Electromagnetics Laboratory 3

1 Purpose and Learning Objectives

1. Analyze a simple circuit with an ideal transmission line.

2. Analyze Rogers Corporation PCB data sheets

3. Find ADS LineCalc utility

4. Familiarize yourself with LineCalc

5. Name and set different substrate parameters in LineCalc

6. Describe different parameters and explain how they affect the impedance and length of themicrostrip line

In the first lab this semester, we analyzed how one type of transmission-line, a coaxial cable,affects the delay (aka phase) of the signal between the generator and the load. In this lab, we willanalyze how transmission-lines affect voltage and current time-delay and input and output impedanceof a simple circuit. We will first look at an Ideal transmission line in ADS, and then we will lookat another transmission line, a microstrip line used in high-frequency Integrated Circuits (ICs) orHybrid Circuits. Integrated Circuit (IC), aka ”chip”, means that all circuit elements are built on asilicon chip. For example, in computers, ICs are memory chips or processor chip. You have also seenan OPAMP IC 741 in the EEE 117L. A hybrid circuit means that the ICs (chips) are connected ona PC board using microstrip lines.

2 Ideal Transmission Lines

In this section, we will see how lossless transmission lines affect signals in a circuit. Ideal transmissionlines do not exist. They are ideal elements used in ADS to help us focus on essential conceptswithout getting into details about how the transmission line is built. The only two parameters oftransmission lines that we will use in this section are the electrical length of a transmission line (E)and the impedance of a transmission line (Z0).

2.1 Electrical Length and Transmission-Line Impedance

2.1.1 Electrical Length of the line in meters

We’ve learned that λ = cf√εr

, and that β = 2πλ

.

There’s more. The line length is typically expressed in terms of the fraction of the signal’swavelength.

California State University Sacramento EEE161 revised: 31. January, 2021


l = Nλ (1)

Typically, but not always, N is a fraction, for example, N = 12

= 0.5, N = 14

= 0.25 orN = 1

8= 0.125; although it can be any number. The length of the line is then written as

l =λ

2= 0.5λ (2)

l =λ

4= 0.25λ (3)

l =λ

8= 0.125λ (4)

If the line is l = λ4

at 1 GHz, we say: ”This line is quarter-wavelength long at 1 GHz”, meaningone-quarter of the wavelength fits on the line. We could also say that the line is physically 7.5 cmlong, as the wavelength is λ = 30 cm at 1 GHz, but you will not hear anybody say that a line is7.5 cm long.

When we say quarter-wavelength long, we refer to the line’s physical length at a specific frequencyin meters.

2.1.2 Electrical length of a line in degrees

We saw previously how transmission-line delays the signals between the generator and the load. Thereason for this delay, as we’ve seen, is that the signals propagate with finite speed, about 30cm pernanosecond (v = 30 cm/ns), or 12 inches per nanosecond (v = 12 in/ns), and need time to get fromthe generator to the load. For example, a signal needs 1ns to get from the generator to the load if itis connected by a 30cm line (t = l

v= 30

30= 1 ns). We can use the simple v=l/t formula to find the

time lag, but how can we find how many electrical degrees is that? To express this time delay interms of electrical degrees, we use β, the transmission-line phase constant, multiplied by the physicallength of the line l (Θ = βl). In ADS, this electrical length in degrees is labeled as E.

The phase shift between input and output signal on a transmission line is Θ = β ∗ l. β (beta) iscalled the phase constant. It represents the spatial frequency of the signal. Θ = β ∗ L is the phasein degrees or radians (related is a time delay in seconds). Θ can be, for example Θ = 450, Θ = 900,Θ = 1800. Θ is a function of frequency, because β is a function of frequency. If Θ = 900, we say:”The line is 90 degrees long at 1GHz”, meaning the output signal at 1GHz will be shifted for 900 withrespect to the input signal. When we say 900, we refer to the line’s electrical length, representingthe number of degrees that the line introduces between the input and the output signal.

2.1.3 Transmission-Line Impedance

Transmission-line impedance is a parameter of transmission lines. For example, the first lab’s coax-ial cable had a transmission-line impedance of Z0 = 75 Ω. Typical values for this impedance areZ0 = 50 Ω, Z0 = 75 Ω, Z0 = 100 Ω, and some older transmission lines, such as two-wire lines hadtransmission line impedances of Z0 = 300 Ω, or Z0 = 600 Ω.



2.1.4 Examples

1. What is the electrical length of a 30 cm line in terms of the fraction of wavelength at 1 GHz?What is the electrical length of the line at 1GHz?

Wavelength at 1 GHz, assuming the wave is propagating in air is λ = cf

= 30 cm. Since the line

is also l=30 cm long, the length of the line in terms of wavelength is lλ

= 1, or l = λ.

The electrical length of the line is θ = βl = 2πλλ = 2π = 3600.

2. What is the electrical length of a 15 cm line in terms of the fraction of wavelength at 1 GHz?What is the electrical length of the line at 1GHz?

Wavelenght at 1 GHz, assuming the wave is propagating in air is λ = cf


is 15 cm long, the length of the line in terms of wavelenth is lλ

= 12, or l = λ

2.

The electrical length of the line is θ = βl = 2πλλ2

= π = 1800.

3. What is the electrical length of a 7.5 cm line in terms of the fraction of wavelength at 1 GHz?What is the electrical length of the line at 1GHz?

Wavelength at 1 GHz, assuming the wave is propagating in air is λ = cf


is 7.5 cm long, the line’s length in terms of wavelenth is l = λ4.

The electrical length of the line is θ = βl = 2πλλ4

= π/2 = 900.

2.2 AC simulation of an Ideal Transmission Line in ADS

In this section, we will simulate an ideal transmission-line circuit Figure 1 using the AC simulationto find the total voltage and current at the input and output of the transmission line.

AC simulation is a frequency-domain simulation, and we are only observing voltages and currentsin their steady-state. In AC simulation, the circuit elements are simulated in the frequency domainas impedances.

In lab 1 we used Transient simulation, a time-domain simulation, and we can observe both steady-state and transients. In time-domain simulations, the circuit elements are solved in the time domainas differential equations. Time-domain simulations are more computationally intensive.

Figure 1: Transmission line terminated in a load.



2.3 Building a transmission-line circuit in ADS

Build a circuit, as shown in Figure 2. The TLIN is under Transmission Lines- Ideal palette. Notethat in this circuit, we only display one conductor of the transmission line. We are assuming thatthe other line is part of the ground, and we don’t have to add it to the schematics. Check that theAC simulation is set to a Single Point - 1GHz. Then, display the results using a table, as shownin Figure 3, and polar plots. Plot input voltage and input current on one polar plot, and outputvoltage and output current on another polar plot. Multiply the current by 10, to see both voltageand current clearly on the plot, as shown in Figure 4.

1. Use eLi the iCe man or CIVIL to confirm that the voltages and currents are leading or lagging.From this information, conclude the type of impedance at load and input. (Is it inductive orcapacitive.)

2. Write an equation for impedance on the Data Display window in ADS. Display the impedancein a table on the Data Display window. Verify that your answer to the previous question isconfirmed.

3. Are the input and load impedances the same? Why so, or why not?

Figure 2: AC simulation in ADS of the circuit shown in Figure ??.



Figure 3: AC simulation of voltage and current at the input and the load of the circuit shown inFigure 2.

Figure 4: AC simulation of the load voltage and current on a polar plot. The circuit is shown inFigure 2.



2.4 Analysis of results for transmission-line problem 1

Answer the following questions:

• In a table, compare the simulated: input impedance, load impedance, input voltage, inputcurrent, output voltage, and output current. Discuss how are the impedances, voltages, andcurrents different and how they are the same.

3 Microstrip Lines

Microstrip line, shown in Figure 5, is a type of transmission line typically used in high-frequencycircuits. It consists of a thin copper line on top of a dielectric material, and on the bottom of theline is a copper sheet.

Figure 5: Microstrip Transmission Line.

The microstrip line was invented by D. D. Grieg and H. F. Englemann in their paper: ”MicrostripA New Transmission Technique for the Klilomegacycle Range”. They got the idea when they observedthat the fields of a two-wire line are the same as fields of a conductor above the ground plane, asshown in Figure 6. To simplify manufacturing, the top line was then made to be rectangular insteadof cylindrical.

Figure 6: Invention of Microstrip Line by Grieg and Engelmann.

The simulated electric and magnetic fields in Ansys HFSS of a microstrip line are shown in Figure7 .



(a) Microstrip line electric field vectors.

(b) Microstrip line electric field streamlines and magnetic field vectors.

Figure 7: HFSS simulation of Microstrip line vector fields.



4 Using Matlab to design microstip lines

Sacramento State students, when logged in to GlobalProtect VPN can download Chapter 6, of thefollowing book from the IEEE web site: Foundations for Microstrip Circuit Design, Terry C. Edwards;Michael B. Steer. Look at Section 6.7 Formulas for Accurate Static-TEM Design Calculations.

There are two different cases that we want to consider, Synthesis and Analysis.In Synthesis, where we know the transmission-line impedance Z0 and electrical length E of the

line, from our ideal transmission-line simulations, and we want to find the physical width (from thetransmission-line impedance Z0) and physical length (from electrical length E).

In Analysis, we know the physical width (w) and length (l) of a transmission line, and we wantto find the transmission-line impedance Z0 and electrical length E of the line.

In this lab, we will only look at Synthesis equations.

4.1 Synthesis

Edwards book separates calculations into two different sets of formulas depending on whether theline is low impedance Z0 > (44 − 2εr) Ω or high-impedance line, when Z0 < (44 − 2εr) Ω. To seewhich set of formulas to use, first look at the transmission line impedance you want to use and therelative dielectric constant. For example, if the transmission line impedance is 50 Ω, and the relativedielectric constant is εr = 10, then 44− 2εr = 44− 20 = 24. In this case 50Ω > 24, so you would usethe first set of equations below.

4.1.1 Z0 > (44− 2εr) Ω

We will start with high-impedance (narrow) strip Z0 > (44− 2εr) Ω. We are looking for the ratio ofthe microstrip’s width to the height of the substrate first. The w/h ratio depends on the parameterH ′, which has nothing to do with the substrate’s height. We will first find H ′, then use it to find theratio of the microstrip’s width to the height of the substrate and effective dielectric constant.

H ′ =Z0

√2(εr + 1)

119.9+

1

2

(εr − 1

εr + 1

)(lnπ

2+

1

εrln

4

π

)(5)

w

h=

(eH

′

8− 1

4eH′

)−1(6)

εeff =εr + 1

2

[1− 1

2H ′

(εr − 1

εr + 1

)(lnπ

2+

1

εrln

4

π

)]−2(7)


https://ieeexplore.ieee.org/book/7906179

https://ieeexplore.ieee.org/book/7906179


(a) Microstrip line dimensions, width (W) and length (L). Width of the line dependson the transmission-line impedance Z0 and the length on the electrical length ofthe line Θ.

(b) Microstrip line thickness (t) and dielectric thickness (H).These parameters are given in PCB Data Sheets.

Figure 8: Microstrip Transmission Line dimensions.



4.1.2 Z0 ≤ (44− 2εr) Ω

dεr =59.95π2

Z0√εr

(8)

dε1 =59.95π2

Z0

(9)

w

h=

2

π[(dεr − 1)− ln (2dε1 − 1)] +

εr − 1

πεr

[ln (dεr − 1) + 0.293− 0.517

εr

](10)

εeff =εr

0.96 + εr(0.109− 0.004εr)[log(10 + Z0)− 1](11)

4.1.3 Physical length from electrical length

To convert electrical length to physical length, l = θ2πλ

= θλ2π

rad, or l =(θλ360

)deg, where λ =

c/(f√εeff ).

4.2 Example problem: Compute width and length of a microstrip line

Using the above formulas, find the width and length of the transmission line from the AC simulationin Figure 2, on a substrate with relative permittivity εr = 9.6 with thickness h = 10 mil. Note thatunit ”mil” is not a millimeter, it is a one-thousandth of an inch.

5 Using Line Calc to design microstrip lines

We will use LineCalc in ADS to find the width and length of a microstrip transmission line on thesame example as in Section 4.2.

Using LineCalc, find the width and length of the microstrip transmission line from the AC sim-ulation in Figure 2, on a substrate with relative permittivity εr = 9.6 with thickness H = 10 mil.LineCalc uses more complicated equations than what we used in the previous section, so additionalsubstrate parameters are assigned. Set the thickness of the metal T = 1.4 mil, dielectric loss totan δ = 0.001, copper conductivity to Cond = 4.1E7. Then, compare the width and length ofmicrostrip lines from LineCalc with values found from equations in Section 4.

1. Start ADS. In schematic window, click on Tools, Line Calc, Start Line Calc. LineCalc windowshould open. Choose the microstrip line (MLIN).

2. Design a 50 Ω, 60o line from Figure 2, for the given substrate. Hint: For this substrate, youshould get from LineCalc that the width of the line is w ≈ 8.4mil, and the length L ≈ 804.4mil.

Compare the values you got from LineCalc and Edward’s equations for 50Ω, 60o line. Calculateabsolute and relative error and present them in a table.



Figure 9: Calculating length and width of a microstrip transmission line using Line Calc.



6 Simulation of Microstrip Line in ADS

1. Open the circuit with the transmission line you used at the beginning of the lab.

2. Go to TLines-Microstrip from the pull-down menu. Select MSUB and place it on the schematic.

3. Set the substrate parameters in MSub to what the substrate parameters are.

4. Use MLIN for transmission lines as shown in Figure 10. For Microstrip lines, you have to enterthe actual width and length of the lines. The line’s width depends mainly on the transmissionline impedance, and the length of the line depends mainly on the electrical length. Both are afunction of the type of substrate used.

5. Make a circuit with a generator, microstrip line, and the load.

6. Use the values for width and length of your line from the previous step.

7. Simulate the circuit and compare the voltages and currents for ideal transmission-line andmicrostrip line in a table. Don’t forget to compare both magnitude and phase of both voltageand current.

Figure 10: Microstrip transmission-line matching circuit example.



7 Working with manufacturers PCB Data Sheets

Where do we get information on dielectric constant, dielectric loss, the dielectric thickness of actualsubstrates we can use? Engineers use PCB datasheets.

Go to the Rogers Corporation website, then go to the Advanced Circuit Materials link and findthe appropriate substrate parameters (εr, tanδ) for RT Duroid5870 and RO 4003C. For each, find twothicknesses of the substrate 62mils and 32mils, and pick the thickness of the metal that is describedby the weight of copper on a square inch, for example, 1/2 oz, 1 oz, 2 oz EDC copper. If the dielectricthickness is not available exactly as specified, select the closest value commercially available. Thismeans that you will have to find four different laminates. To find these parameters, look at theHigh-Frequency laminates - Product selection guide. Make a table, and write the specifications ofthe substrates you found. Include dielectric constant, the thickness of the substrate, the thickness ofmetal (with both physical thickness and per oz of copper), dielectric loss, roughness of the dielectric(use rougher side, usually dielectric side). Put all parameters in a table. Use LineCalc to find thewidth and length of a 50Ω, 60o line on each substrate.


eee161 applied electromagnetics laboratory 3

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