Single Time Constant Measurement ECE 2100 Dr Len
- Slides: 31
Single Time Constant Measurement ECE 2100 Dr. Len Trombetta and Dr. Dave Shattuck & additional note Dr. Han Le 1
If electrons from a source are blocked from making a round trip of a circuit, or even entering into a device, can the source supply power to the device? Han Q Le©
Capacitors There are many different types of capacitors. Your lab kit has ceramic and electrolytic capacitors. ceramic electrolytic These can have large capacitance values and support large voltages. The dielectric is an electrolyte (ionic fluid). The polarity must be positive at the longer lead (not shown in figure). These can have small values, and the value is more stable over large voltage and frequency ranges. Polarity is not important. The dielectric is a ceramic. http: //en. wikipedia. org/wiki/Capacitor 3
Han Q Le©
Capacitor Types Why so many capacitor types? The various capacitors types trade off performance : • Capacitance • Usable voltage range • Variation in capacitance with temperature or frequency • Leakage current (how long it will hold a charge) 5
Han Q Le©
Han Q Le©
Capacitor Values The electrolytic caps usually just state the value, e. g. , 100[m. F] [p. F] = 10 -12 [F] [n. F] = 10 -9 [F] [m. F] = 10 -6 [F] The ceramic caps are more like resistor codes. For example: 104 Z 151 J Ignore the letter and interpret the numbers as you would the resistor code. This is the value in [p. F]. Examples: 104 Z: 10 x 104 [p. F] 151 J: 15 x 101 [p. F] = 105 x 10 -12 [F] = 150 x 10 -12 [F] = 10 -7 [F] = 0. 1 [m. F] = 150 [p. F] = 0. 15 [n. F] 8
Capacitor Tolerance Most capacitor codes will not state a tolerance, but it is usually around 20%. If you need an accurate value, use the meters in S 385 near the TA bench. 9
Pre-Lab We will do the Pre-Lab in class. Write answers to the Activities in your Lab Notebook. This is the same RC as in the first part of your lab, except that the output is across C, whereas in the lab handout it is across R. 10
Capacitor Energy Storage (cont. ) An alternative calculation for the energy of a capacitor is the stored energy of the electric field. The energy density of an EM field is: Hence, for a capacitor: Han Q Le©
The Analysis Part I: Charging Assuming the switch was at b) for a long time and moved to a) at t = 0, find the voltage vc(t) for t ³ 0. This is the step response. 12
Click on these links for amusing illustration or demo Han Q Le©
Two basic RC circuit configurations Frequency Response or, integrator R input vin[t] Frequency Transfer Function C i(t) output vout[t] differentiator C input vin[t] Han Q Le© i(t) R output vout[t]
This app has both RC filters. It illustrates the concept of Fourier synthesis (which is not in this course but useful for you to get acquainted). Follow instruction to see output of square pulse input. 2: slide to change pulse duration 1: select square pulse, (you can select others just for fun) 3: select 30 Fourier components Click this for RC integration input Fourier components Click this for RC differentiation Han Q Le© 4: slide RC time and observe output Fourier components
This is an integrator The Plot Part I Answer: Activity 1: Plot the function vc(t) vs. t in your lab notebook. See below for details. Use your calculator to find actual points on the graph – do not just sketch by “eyeball”. Use these parameters: Vs = 5[V] R = 47[k. W] C = 0. 022[m. F] Choose a horizontal scale factor so that you have at least 10 time constants (10 t = 10 RC) across the paper (see below). Paper in landscape position vc(t) Put your first plot in this side We will plot something else here later t~5 t t t~10 t 16
What’s the 10 t thing? When t = 5 t in the equation above, the voltage v. C(t) has (almost) completely stopped changing – we are in “steady state”. So to be sure we are plotting for a long enough time to see the whole charging function, we need to plot from 0 to at least 5 t. For the second function (coming up next) we need to plot for another 5 t to see the complete discharge function. Paper in landscape position vc(t) Put your first plot in this side t~5 t t t~10 t 17
The Analysis Part II: Discharging t = t 1 Now assume that the switch stayed in position a) until time t 1, which was a long time. If it then moves to position b), find the voltage vc(t) for t ³ t 1. This is the natural response. 18
The Plot Part II Answer: t ³ t 1 Activity 2: Plot the function v. C(t) on the same graph (see below): • Vs = 5[V] R = 47[k. W] C = 0. 022[m. F] • t 1 = wherever you stopped the first plot – this should be 5 t. This plot should be a continuation of the first one. . . vc(t) t = 0 t = t 1 t t~10 t Plot the function above here. 19
Graphical Analysis Look at your second graph (the “discharge” curve), which is described by Activity 3: i) Substitute t – t 1 = tc into this equation. Then Please see this slide also for additional note. • What value does e-1 have? Compare this with 3/8. • What is the value of vc(t) at this time? ii) Find this point on your graph and label it. iii) Find the corresponding point on the first graph (the “charging” curve) by substituting t = tc into the charging equation. 20
The Experiment Now imagine the switch moving back and forth from a to b, over and over, staying in each position long enough to arrive at “steady state” – in other words, for 5 time constants in each position. We can accomplish this be applying a square wave to the circuit input. Activity 4: Apply a square wave going from 0 to 5[V] to the input of the circuit. Connect the output to the scope. Use the “T” connector on the lab bench to view the input and the output on the scope. Compare what you see on the scope to the plot in your lab notebook - they should be the same! Function Generator Scope 21
dc Offset To have a square wave that goes from 0 to 5[V] instead of -2. 5[V] to +2. 5[V], you will need to use the dc offset. Remember that the dc offset you actually get on the scope will be twice what is stated on the function generator. Verify that you have 0 to 5[V] by examining the scope screen and looking at the vertical sensitivity. 22
The Measurement… The screen has 8 divisions vertically, so if we could get the discharge curve to cover the entire screen, like this… Oscilloscope Screen …we could simply locate the point where the curve crosses the value 3/8. The corresponding time would then by t = tc. 23
The Technique But how do we get the curve to be exactly 8 divisions tall? The vertical scale has a feature called “fine”… Get close to full-screen and then adjust using “Fine”. Select or de-select “Fine” Select CH 1 (or CH 2) 24
Let’s Do It! Activity 5: Using the response on the oscilloscope that you got in Activity 4, isolate the discharge curve, and measure the time constant. 1. Use the fine vertical scale adjustment to get the curve to cover the entire 8 divisions on the screen. 2. Make sure your square wave period is at least 10 time constants so that you have a full charge or discharge cycle. 3. What would the corresponding point on the charging curve be? 25
An Alternative We don’t have to do it that way. We have an equation, which is “plotted” on the screen. If we measure any value of vc(t 0) and the corresponding time t 0, we can solve for the time constant. 26
Statistically rigorous analysis of the exponential decay time Han Q Le©
Same signal linear scale log scale ONLY ONE data point is used – referenced to peak and floor when we use 1/e rule, or 3/8 -rule, we use only one data point, which must also be referenced to a peak value and a floor value. This is highly susceptible to error. convenient, but NOT most accurate. Han Q Le© finding the slope between 2 cursors on a log scale with linear regression results in less uncertainty (using many data points) and impervious to errors in peak and floor points. more work, but most accurate.
For lab report • Obtain the value of RC time constant with the 1/e-rule from the scope. • Save the data from the scope in. csv format • Use the app given or you can use Excel to convert the amplitude into its log value, then plot. • Select any two cursors that include a wide range of data points on the exponential decay portion of the signal (see previous slide), then perform linear regression. • The slope is the negative inverse RC time (-1/RC), compare this value to the one you obtain with the 1/erule. Print the log-plot regression graph from the app, cut, and glue or stapled the plot to your lab report. Han Q Le©
And Another Thing… You may find it convenient to use the external triggering (EXT TRIG) feature of the scope for this lab (or any lab, for that matter). You can review the “ECE 2100_Fn. Gen_Scope” presentation posted on the class web site. 30
Things You Should Know • How to set amplitude, offset, and period using the function generator. • How to read amplitude, offset, and period directly from the scope factors (not using the “measurement” function). • How to use “coupling” (ac, dc). • How to use the trigger menu. • How to use the “fine” adjust to get a fullscreen waveform. 31
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