ELEC 477/677L Wireless System Design Lab Spring 2011

Lab #3: LC Impedance-Matching Networks

Introduction

Most wireless systems are comprised of several subsystems (subcircuits) that are connected together to accomplish a specific task. For example, a wireless receiver typically consists of amplifiers, filters, mixers, and other circuits all operating together as a unit. An important consideration in RF system design is to ensure that the input of each stage presents the proper load impedance to the preceding stage and that the output impedance of the stage is appropriate to feed the following stage. This might be necessary to ensure maximum power transfer between stages. Also, most filters require very specific source and load impedances (sometimes very different from the standard 50 Ω) in order to operate properly. The process of changing an effective source or load impedance from one value to another one is called impedance transformation, or impedance matching. One way to match impedances is to insert an L network consisting of one series reactive element (an inductor or a capacitor) and one shunt reactive element between the stages. In this lab exercise, you will design and test an L-shaped network to transform a load impedance to 50 Ω.

Experimental Procedure

Your deliverable for this lab session will be an e-mail message containing the items specified below. It is due before the next lab session. Grades will be quantized in 5-point intervals on a 100-point scale.

· Design an L network to match a load resistance of 300 Ω to the source impedance of the bench top function generator or signal generator (both 50Ω) at an operating frequency of 10MHz. The load impedance simulates the radiation resistance of a folded dipole antenna fed with standard 300-W “twin lead” (a parallel-wire transmission line commonly used with consumer FM radio receivers). Include the inductor and capacitor values and each component’s location (i.e., in series with the source or load, in parallel with the source or load) in your email message. Also include the Q (quality factor) of your matching network.

· Calculate the input impedance of the matching network/load impedance combination over the frequency range 1-30 MHz using Mathcad or Matlab, and use the results to plot the VSWR (with respect to 50Ω) over that range. You do not have to plot VSWR values over 10:1. On a separate graph, plot the real and imaginary parts of the input impedance over the same frequency range. Include axis labels with units (if any), a legend, and a title for both plots.

· Build the L network using the components available to you on a prototyping PC board that will be provided. The inductor should be wound on a toroidal iron powder core. Information on these cores is available at the Amidon Associates web site, which is linked on the laboratory web page. The required capacitance can be approximated using series and/or parallel combinations of standard capacitor values, although you should try to use just one to save space and keep lead lengths short. Leave two terminals to which the twin lead can be soldered, and use a board-mounted coaxial connector for the input connection.

· Use one of the handheld impedance analyzers to plot the VSWR vs. frequency over the same range for which you calculated the VSWR using circuit analysis. You will have to copy the displayed data manually into Mathcad or Matlab. Eight to ten data points, including the point of best match, should be sufficient; more would be better. Again, you do not need to record VSWR values above 10:1. Plot the measured VSWR data along with the predicted VSWR data on the same graph using the Mathcad or Matlab. Save an electronic copy of the plot, and include it in your e-mail message.

· Answer the following thought questions in your e-mail message:

o Besides measurement error, what other factors might account for any differences you see between the measured and predicted VSWR data?

o For the center frequency fo of 10 MHz, does the formula fo/Q match the observed 2:1 VSWR bandwidth of your matching network?