431-301 Electrical Network Analysis and Design

The University of Melbourne, School of Engineering

Electrical Network Analysis and DesignWorkshop 7: Design of Antenna to Achieve Maximum Power Transfer using SPICE Simulations of Two-Port Networks

(Week beginning 12th May 2014)Welcome to Workshop 7 for Electrical Network Analysis and Design. This workshop introduces you to the analysis of 2-port networks. You will investigate y parameter and a parameter calculation through circuit simulations in Linear Technologys LTSpice. You will use these parameters to design an optimum antenna for connection to the 2-port network in terms of maximum power transfer.

The lab has a pre-workshop component which should be completed prior to attending the workshop. It is also advised to read through this entire Workshop 6 document to prepare for the lab.Part A: Pre-workshop

1 Theoretical calculations of y- and a- parameters for a two-port networkThe y-parameters of a two port network are the admittance parameters that satisfy the equations:

(1)

(2)

where is the voltage across port 1, is the voltage across port 2, is the current flowing into port 1 and is the current flowing into port 2. From equations (1) and (2) we can find the expressions in Table 1.

S S

S S

Table 1: y-parameters

(a) Show that the s-domain expressions for the y-parameters of the 2-port network shown in Figure 1 are:

(3)

(4)

(5)

(6)

Hint: Since the 2-port is symmetric and reciprocal we only need to calculate 2 parameters since =and .There are 2/10 marks for successful completion of this exercise.

Figure 1: 2-port network

The a-parameters define the transmission between the ports of a 2-port network. A definition of a-parameters is given in Table 2, with parameter conversion equations from y-parameters to a-parameters provide in Table 3.

S

Table 2: a-parameters

S

Table 3: y-parameters to a- parameter conversion

Reference:

J.W. Nilsson and S.A. Riedel, "Electric Circuits", Chapter 18, 9th edition, Pearson Prentice-Hall, 2010. Part B: LTSpice Circuit Simulation Exercises For this exercise the following equipment is required from the lab kit:

PC running LTSpice3. Using LTSpice to build and simulate circuitsStarting LTSpice and creating a new Project 3. (a)From the Start Menu, select the LTSpice program.Start Menu > All Programs > - Department Specific Apps - > EE Specific Apps > LTSpice3. (b)You will need to create a new project. The procedure is the same for any circuits you will simulate. Select:File > New Schematic (Default file names are Draft1, Draft2, etc, so it would be a good idea to save your files with sensible names like Two Port Simulation 1).

IMPORTANT: Ensure that you DO NOT create your projects on the local PC hard disk, as these files will potentially be erased when you log out. Instead, create your projects in your allocated account directory or on personal portable hard drive.

Click OK to save the file.Building Circuits in LTSpice 43. (c)To add components to the schematic, use the Edit menu:

Edit > select required part from the list Click on the schematic window to place the part. Press the escape key (ESC) to stop placing parts. Control-R can be used to rotate parts to their desired orientation.

Right-click on a part to enter/modify several parameter values, or alternatively, right-click on the text of individual parameter components (Names, values, etc) to modify these elements. LTSpice understands common letter abbreviations, for example 10k is interpreted as 10,000. Common abbreviations can be found in Table 4. (However, be aware that case is ignored, so both 'M' and 'm' refer to milli, and not Mega)

Spice SymbolNumberCommon Name

109"G" or "g"giga

106"MEG" or "meg"mega

103"K" or "k"kilo

10-3"M" or "m"milli

10-6"U" or "u"micro

10-9"N" or "n"nano

10-12"P" or "p"pico

10-15"F" or "f"femto

Table 4: Common Spice Symbol AbbreviationsAlso note that all element names must be unique. Therefore, you cannot have two resistors that are both named "R1",for example, as this will cause the following error in your simulation:Netlist error: Duplicated Instance Name, R1 in /PATH/filenameGround parts can be drawn using Edit > Place Ground (or 'G' key). The following error message will appear during simulation if the ground symbols are not included: This circuit does not have a conduction path to ground! Please flag a node as ground.Wires can be drawn using Edit > Draw Wire (or F3 key). Click on the nodes of one component to start a wire and click on the node of a second component to draw a wire between them. Press the escape key (ESC) to stop placing wires.

Sources (voltage, current, etc) can be obtained from the Edit > Component (F2) category. For instance, to place a 5V DC source, select the voltage item. Upon right-clicking, it's default arrangement of DC value and series resistance (if required) may be entered.

To obtain a sinusoidal (or more complex) source, the 'Advanced' option should then be selected, providing the ability to modify the waveform that is generated (pulses, frequencies, delays, etc, depending on the source that is required).Simulating Circuits in LTSpice3. (d)To simulate you will need to build a simulation profile, depending on the type of analysis you wish to carry out. For example to simulate the transient response you will need to create the corresponding simulation profile by selecting:

Simulate > Edit Simulation Cmd

The pop-up window requires that you select an analysis type (i.e. Transient) and select some simulation properties. A guide to get you started would be:

Analysis Type = Time domain (Transient)

Stop Time= 10s

Max. Timestep = 1ms

To simulate click on the play button (running man icon) or select:

Simulate > Run

Viewing Simulation Results in LTSpice3. (e)Once the run icon is selected, a new window representing the simulation results appears. To obtain a voltage trace, a probe may be placed at any point on the circuit by hovering and left-clicking. Currents can be obtained by clicking on a component terminal.

In the plotting window, any other signals within the circuit can be viewed using:

Plot Settings > Add Trace (Ctrl-A)The Add Trace dialog box also allows various mathematical operations with the signals in the circuit, for example I(R1) + I(C1): the current through component R1 added to the current through component C1. 4. 2-Port Circuit Simulation4. (a)Construct a schematic of the 2-port network in Figure 1, with a sinusoidal voltage source at port 1 and a short circuit at port 2, as shown in Figure 2. To obtain the sinusoidal source:

Edit > Component (F2) > voltage > Advanced

Establish a 'Sinusoidal' source to have a 0V DC offset, an amplitude of 10V and a frequency of 10Hz. Let the internal source resistance be modelled by Rg=1. You can add the port1 and port2 labels using Edit > Label Net (F4), and clicking on the relevant wire after entering the label name. Net labels are useful for identifying signals using Trace > add Trace in the plot window.

Figure 2: 2-port network in LTSpice Schematic

4. (b)Run a transient sweep as detailed in 3 (d), using the transient parameters:

Run Time= 10s

Start saving data after= 0s

Max. Step size= 1ms[Note: once the transient parameters are entered, you will notice the .tran directive appear in the schematic window]

4. (c) i.Use the information in Table (1) to determine the y parameters of this circuit from the simulation results. You can probe signals on the circuit as described in section 3(e). As we are dealing with AC signals the ratios of voltage and current can be computed using the amplitudes of the relevant voltages and currents. You will need to use the zoom and toggle cursor buttons in the plot window. Hint: Remember that this is a symmetric and reciprocal 2port so you will only need to find 2 of the 4 y parameters. There is 2/10 marks for successful completion of this exercise.

4. (c) ii. Compare your result with those expected in theory using the equations you found in 2(a). Hint: set , where , is , with the input frequency of the circuit which is 10Hz here.There is 1/10 marks for successful completion of this exercise.4. (d)Use the information in Table 2 to determine the a parameters of this circuit from the simulation results. Again remember that due to a symmetric and reciprocal network, only 2 of the 4 parameter need to be found from the simulation.

There is 1/10 marks for successful completion of this exercise.4. (e)Compare your results in 4. (d) to those theoretically expected using Table 3 and the theoretical y parameter results from 4 (c).

There is 0.5/10 marks for successful completion of this exercise.5. Design an antenna as the output termination of our 2-port network. Our 2-port network will be connected to a radio antenna, which we will model as a load impedance. We would like the maximum power to be transmitted to the load to allow our radio signal to travel over the largest distance possible. Your task is to design a suitable load resistance to allow maximum power transfer to the load.

Figure 3: Terminated 2-port network in LTSpice schematic5. (a)Add a load resistor to port 2 of the circuit as shown in Figure (3), first set the resistance to a default value of 10. Run a transient simulation for 10 seconds.

5.(b)What is the average power delivered to the default 10 load? You can find this by going to the plot window and choosing Trace > add trace. Use the trace setting box to plot a signal for the average power in component RL. Take the average power value to be the value in steady state after initial transients.

There is 0.5/10 marks for successful completion of this exercise.

5. (c)Confirm the power value obtained in simulation was that expected in theory. Recall from lecture notes that , and that . To find I2, we find the following a parameter equations from Table 18.2 (Nilsson & Riedel) & lecture notes: .

There is 1/10 marks for successful completion of this exercise.

5. (d)Use LTSpice simulation to design an antenna load impedance that allows for maximum power transfer to the load. LTSpice can be used to make a parameter sweep of values and plot the resulting power against . To perform a parameter sweep:

(i) Change the component value of from the 10 default to a variable called {RLVAR} (Note that you must include the curly brackets, which indicate to LTSpice that the value of the resistor is a global parameter called RLVAR. To modify a components attributes, Control-Right Click the component, and edit the desired value, and click OK to save)(ii) In order to use RLVAR in a parametric sweep it is necessary to Edit Spice directive and enter the .STEP instruction. To do this, choose Edit > SPICE Directive and in the text box, enter:.step param RLVAR start_value end_value stepsize

Choose to sweep over resistance values 0.1 to 10 in increments of 0.1. LTSpice will automatically perform the simulation over and over, using a new value forRLVARduring each run.

(iii) Run the simulation (Note: if there are memory issues, you can change the stepsize in the above parameter/directive to a slightly larger value, such as 0.3, to reduce space requirements)

5. (e)When the simulation is complete, in the plot window choose

Plot Settings > Add Trace (or Ctrl-A)

The goal is plot power against . Recall from 5(b) that the average power value fluctuates at the start of the simulation and before converging to a steady state value. Therefore we wish to plot the power value at the end of the simulation time, t=10s.

In the Add Traces dialogue box, enter an expression to represent the average power.

To modify the x-axis variable from the present variable of time, double-click the horizontal axis, and modify the 'Quantity Plotted to V(port2)/I(RL) (This will effectively convert the x-axis into the resistance units of the parameter RLVAR).

5. (f)From the plot in 5(e), find:

i. the load impedance you need your antenna to have for maximum power transfer

ii. the maximum power delivered to this antenna.There is 1/10 marks for successful completion of this exercise.5. (g)Use the a parameters to find theoretical values for (i) and (ii) in 5(f). Hint: the load resistance for maximum average power transfer equals the conjugate of the Thvenin impedance w.r.t port 2 and from Table 18.2 (Nilsson & Riedel) & lecture notes we have that:

.There is 1/10 marks for successful completion of this exercise.Created by Elma OSullivan-Greene, 2010.

LTSpice adaptation by Andrew Gdowik, April 20131