Wireless and Microwave Instructional Laboratory


Laboratory #3 Notes


The purpose of this laboratory exercise is to introduce you to the following:
1. Harmonic Balance, Power Budget, and Frequency Characterization Simulations using Advanced Design System (ADS)
2. Communication System Design Techniques for Optimal Image Frequency Rejection and Noise Figure
3. The Principles of Mixing
4. Re-emphasis of the use of dB, dBm Units

For this exercise you will need to turn in the following items:
1. One-Page Post-Laboratory Report Including Summary and Discussion Pertaining to Topics Listed in the "Laboratory Report" section of the experiment
Note: Please omit Part 4(c) given in the "Laboratory Report" section. No power budget was performed at the image frequency in this experiment.
2. Worksheets Containing Results
3. Printouts and Tables as Specified in the "Laboratory Report" section of the experiment.

Please Note: If you want extra credit for performing optional sections, please make a note of this on your one-page post-laboratory report.

Important Concepts

Mixing

Mixers are imperfect multipliers. Mixers are devices used for downconversion based upon the mathematical principles of sinusoid multiplication.

Example: Multiplication of sinusoidal waves

v1(t) = A cos at
v2(t) = B cos bt

Note that a and b are the radian frequencies of the signals.

v1(t)v2(t) = AB cos at cos bt = (AB/2) cos (a - b)t + (AB/2) cos (a + b)t

It should be noted that the sum and difference of the radian frequuencies a and b of the original signals are present in the resultant signal. This is due to the trigonometric identity

cos x cos y = [cos (x - y)]/2 + [cos (x + y)]/2 (1)

You may have previously been exposed to the identity

cos x cos x = 1/2 + (1/2)cos 2x

which is a special case of (1).

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Image Frequency Rejection

We convert down to an intermediate frequency before converting to baseband by using the principle of mixing. We utilize the mixing of the local oscillator frequency and the desired RF frequency to downconvert the signal to the desired IF frequency. Thus, the local oscillator should be the sum of the RF and IF frequencies. However, another frequency that will produce a difference frequency (with the LO frequency) at the IF is the image frequency, equal to the sum of the IF and the LO frequencies. Thus it is necessary to greatly attenuate the image frequency at the first stage to prevent signal distortion.


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