Trip 3. AC Circuit Analysis
Specific to an AC circuit is the fact that currents and voltages vary in time. For example a voltage could be 1V for a second and then 0V for a second, in a periodic fashion. To understand the complex time behaviour several mathematical concepts must be understood. Measuring AC is a more complex process than DC. The Topnotch Meter will help us determine time variant signals through measurements.
Please click to preview the experiments in this Trip: 1, 2, 3, 4, 5, 6.
![1](javascript:ReplaceContentInContainer('content-exp',' <h3>Experiment 1. Driving an RC Circuit with a Square Wave</h3>
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<img src="./images/Exp1RCsquarewave.jpg" width=" 333 " align=" right" style=" float:right; padding-right:10px; padding-bottom:5px;">
<p> The goal of this experiment is to present an RC (Resistor Capacitor) circuit driven with a periodical square wave. The emphasis is on the ability to model the circuit mathematically as well as to perform a measurement and reconcile the two. From a mathematical point of view, the Laplace transform is needed as well as working with exponential functions.
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<p> It is possible to model the circuit using mathematical software but it is not recommended. It is hoped that student will do the practice exercises and overcome the mathematical content of the experiment. It is also hoped that reconciling theory and measurement is rewarding and gives more confidence.
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![2](javascript:ReplaceContentInContainer('content-exp',' <h3>Experiment 2. Driving an RC Circuit with a Divided Square Wave</h3>
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<img src="./images/Exp2Markers.jpg" width=" 333 " align=" right" style=" float:right; padding-right:10px; padding-bottom:5px;">
<p> The goal of this experiment is to present a more complex RC (Resistor Capacitor) circuit driven with a periodical square wave that is affected by a resistor divider. The mathematical complexity is increasing in this example but can be circumvented by using the circuit techniques studied so far.
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<p> Although the analysis of the circuit is carried out using the Laplace transform, the student is hinted to a sharper, better solution obtained using the Thevenin equivalents.
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<p> The analysis takes into account the difference between the values describing the <b>Topnotch Meter</b> Generator wave and the measured values read by the Mini-Scope.
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![3](javascript:ReplaceContentInContainer('content-exp',' <h3>Experiment 3. AC Analysis of a Low-pass Filter</h3>
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<img src="./images/Exp3LowPass3dB.jpg" width=" 333 " align=" right" style=" float:right; padding-right:10px; padding-bottom:5px;">
<p> The concept of filtering is introduced in this experiment. The goal is to demonstrate the fundamental properties of a low-pass filter. The filter is excited with a wave produced by the <b>Topnotch Meter</b> Generator. The frequency is swept and for each frequency the output of the filter is compared with its input. In the case of a low-pass filter, the waves of low frequency are not changed much by the filter while the waves of high frequency are heavily attenuated. The 3dB frequency is the frequency where the attenuation is 0.707 of the low frequency maximum value. In this experiment the 3dB frequency is 795 Hz. A theoretical analysis is carried out in Matlab to be compared with the measured frequency sweep.
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![4](javascript:ReplaceContentInContainer('content-exp',' <h3>Experiment 4. AC Analysis of a High-pass Filter</h3>
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<img src="./images/Exp4HighPassRC3dB.jpg" width=" 333 " align=" right" style=" float:right; padding-right:10px; padding-bottom:5px;">
<p> In this experiment a different type of filter is introduced. The goal is to demonstrate the fundamental properties of a high-pass filter. The filter is excited with a wave produced by the <b>Topnotch Meter</b> Generator. The frequency is swept and for each frequency the output of the filter is compared with its input. In the case of a high-pass filter, the waves of low frequency are heavily attenuated by the filter while the waves of high frequency are not changed by much. The 3dB frequency is the frequency where the attenuation of the low frequencies is 0.707 of the high frequency max value. In this experiment the 3dB frequency is 603 Hz.
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![5](javascript:ReplaceContentInContainer('content-exp',' <h3>Experiment 5. AC Analysis of a Band-pass Filter</h3>
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<img src="./images/Exp5BandpassRCpeak.jpg" width=" 333 " align=" right" style=" float:right; padding-right:10px; padding-bottom:5px;">
<p> A different type of filter is introduced in this experiment. The goal is to demonstrate the fundamental properties of a band-pass filter. The filter is excited with a wave produced by the <b>Topnotch Meter</b> Generator. The frequency is swept and for each frequency the output of the filter is compared with its input. In the case of a band-pass filter, the waves of low and high frequencies are heavily attenuated. However, in between, there is a band of frequencies which are passed, meaning they are not changed by much. This band of frequencies is determined by two 3dB frequencies low and high, in our case 190 Hz and 3090 Hz. All the filters can be simulated in LTSpice.
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![6](javascript:ReplaceContentInContainer('content-exp',' <h3>Experiment 6. AC Analysis of a Band-stop Filter</h3>
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<img src="./images/exp6BandstopRCFiltercropped.jpg" width=" 333 " align=" right" style=" float:right; padding-right:10px; padding-bottom:5px;">
<p> A different type of filter is introduced in this experiment. The goal is to demonstrate the fundamental properties of a band-stop filter. The filter is excited with a wave produced by the <b>Topnotch Meter</b> Generator. The frequency is swept and for each frequency the output of the filter is compared with its input. In the case of a band-stop filter, the waves of low and high frequencies are passed, not changed by much. However, in between, there is a band of frequencies which are stopped, meaning they are heavily attenuated. The minimum of this band, the notch frequency, is at 637 Hz. </p>
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Experiment 1. Driving an RC Circuit with a Square Wave
The goal of this experiment is to present an RC (Resistor Capacitor) circuit driven with a periodical square wave. The emphasis is on the ability to model the circuit mathematically as well as to perform a measurement and reconcile the two. From a mathematical point of view, the Laplace transform is needed as well as working with exponential functions.
It is possible to model the circuit using mathematical software but it is not recommended. It is hoped that student will do the practice exercises and overcome the mathematical content of the experiment. It is also hoped that reconciling theory and measurement is rewarding and gives more confidence.