Frequency and Time Domain Representations & Introduction to CAD

Introduction

In this lab experiment, we explored the frequency and time domain representations of signals using Mini Circuits Synthesizer signal generator (SSG-6000RC) version 5 and an oscilloscope. Additionally, we delved into the basics of Computer-Aided Design (CAD) software for electronic circuit simulations.

Experimental Setup

For our signal source, we utilized the Mini Circuits Synthesizer signal generator (SSG-6000RC) version 5. This version offers advantages over its predecessors, such as a wideband generator with a 3 Hz frequency resolution and an adjustable output power range of up to 79 dB.

We connected the signal generator to an oscilloscope to observe signal waveforms in the time domain. A 20 dB attenuator was inserted between the signal generator and the oscilloscope to reduce the power level to one hundredth (20 dB attenuation).

We conducted measurements with two different load impedances, 1M ohm and 50 ohm, and observed peak-to-peak voltage for both cases. Notably, the peak-to-peak voltage was observed to be twice as high for the 1M ohm impedance compared to the 50 ohm impedance.

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Peak-to-Peak Voltage Comparison

From the table above, it is evident that the Vpp with a 1M ohm load is 51% greater than that with a 50 ohm load. This difference can be attributed to impedance mismatch and reflections at the signal generator end.

Power and Voltage Relationship

We also examined the relationship between power and voltage. When the power was decreased by 3 dB, there was a 28.22% decrease in peak voltage. This phenomenon can be explained by the fact that a 3 dB reduction corresponds to a halving of power in watts.

Mathematically, the relationship can be expressed as:

^{V_{peak at -3 dBm}} = ^{V_{peak at 0 dBm}} / √2

For instance, if the power is reduced from 0 dBm to -3 dBm, the peak voltage drops to approximately 70% of its original value.

Nyquist Sampling Theorem

The Nyquist Sampling Theorem states that a sinusoidal signal with a frequency 'F' must be sampled at a rate of at least twice the frequency 'F'. Mathematically, this can be expressed as:

F_sampling ≥ 2F_signal

When we consider a 400 MHz signal, the oscilloscope should ideally sample at 800 MHz to faithfully capture the signal. However, it was observed that a 400 MHz oscilloscope is insufficient for this purpose. At lower frequencies, such as 25 MHz, the signal remains free from distortion and parasitic effects. As the frequency increases, aliasing becomes evident, and the limitations of the oscilloscope's behavior at higher frequencies become apparent.

Frequency Domain Analysis

To overcome the limitations of the oscilloscope at higher frequencies, we employed a spectrum analyzer and signal generator for frequency domain measurements. We set the spectrum analyzer to a center frequency of 400 MHz and adjusted the marker spike to obtain accurate amplitude measurements. By zooming in with a span speed of 20 MHz, we achieved good resolution of amplitude and frequency.

MATLAB Analysis

We used MATLAB to analyze amplitude waveforms. In our experiments, we observed different phase shifts at 0 degrees and 90 degrees. When the phase of s1(t) was adjusted to 0 degrees, both signals were in phase, resulting in constructive interference. Conversely, when s1(t) was shifted to 90 degrees, a phase difference of 90 degrees was introduced, leading to destructive interference and a difference in amplitudes of the combined signals.

Computer-Aided Design (CAD)

As part of this lab, we were introduced to the ADS (Advanced Design System) software for computer-aided design and simulation of electronic circuits. We simulated a low-pass filter circuit using ADS and observed the output waveforms at both S22 and S11 points, gaining insights into circuit behavior and performance.

Conclusion

In conclusion, this lab experiment provided valuable insights into the frequency and time domain representations of signals. We explored the impact of load impedance on peak-to-peak voltage, the relationship between power and voltage, and the Nyquist Sampling Theorem. Additionally, we utilized MATLAB for phase analysis and gained practical experience with CAD software for electronic circuit simulations. These skills are essential for engineers and researchers in the field of electronics and signal processing.