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| university:courses:alm1k:circuits1:alm-cir-cascade-rc [11 Jan 2017 20:44] – created Doug Mercer | university:courses:alm1k:circuits1:alm-cir-cascade-rc [06 Feb 2022 21:11] (current) – [Activity: Cascaded RC low pass filters] Doug Mercer |
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| ======Activity: Cascaded RC low pass filters====== | ======Activity: Cascaded RC low pass filters - ADALM1000====== |
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| =====Objective:===== | =====Objective:===== |
| If two passive RC low pass filters are cascaded the frequency response is not simply the product of the two first order RC transfer functions. This is because the ideal single pole response assumes a zero source impedance is driving the filter and there is no load on the output, i.e. filter drives an infinite impedance. However, directly connecting the second filter acts as a load for the first effectively changing the combined RC time constant. If you try to analyze the cascaded circuit by simply adding phasors you will soon realize the shortcomings of that simple technique. This is where using circuit simulation software is very helpful. | If two passive RC low pass filters are cascaded the frequency response is not simply the product of the two first order RC transfer functions. This is because the ideal single pole response assumes a zero source impedance is driving the filter and there is no load on the output, i.e. filter drives an infinite impedance. However, directly connecting the second filter acts as a load for the first effectively changing the combined RC time constant. If you try to analyze the cascaded circuit by simply adding phasors you will soon realize the shortcomings of that simple technique. This is where using circuit simulation software is very helpful. |
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| As a pre-lab exercise enter the schematic shown in figure 1 into the [[http://www.analog.com/en/design-center/interactive-design-tools/adisimpe.html|ADIsimPE]] circuit simulation, schematic entry software. Three different RC low-pass filter sections are included. The inputs of all three filters are driven by the same AC source V1. Resistor R5 and capacitor C5 form a simple single pole (1st order) filter with the output taken at node dB-0. Resistors R3 and R4 and capacitors C1 and C3 form a 2nd order filter with R4 = R3 and C3 = C1. Two points in this filter should be plotted, the output of the first section at node dB-1 and the output of the second section at node dB-2. Resistors R2 and R1 and capacitors C4 and C2 form another 2nd order filter with R1 = 10*R2 and C2 = C4/10. The two similar points in this filter should also be plotted, the output of the first section at node dB-3 and the output of the second section at node dB-4. This second filter keeps the RC time constant the same for both sections of the filter but reduces the loading effect by increasing the value of the second resistor by a factor of 10 and decreases the value of the second capacitor by a similar factor of 10 (keeping the RC product the same). Using a factor of 10 like this is a good rule of thumb to use when designing cascaded passive RC filters. | As a pre-lab exercise enter the schematic shown in figure 1 into the [[adi>en/design-center/interactive-design-tools/adisimpe.html|ADIsimPE]] or [[adi>en/design-center/design-tools-and-calculators/ltspice-simulator.html|LTSpice]] circuit simulation, schematic entry software tools. Three different RC low-pass filter sections are included. The inputs of all three filters are driven by the same AC source V1. Resistor R5 and capacitor C5 form a simple single pole (1st order) filter with the output taken at node dB-0. Resistors R3 and R4 and capacitors C1 and C3 form a 2nd order filter with R4 = R3 and C3 = C1. Two points in this filter should be plotted, the output of the first section at node dB-1 and the output of the second section at node dB-2. Resistors R2 and R1 and capacitors C4 and C2 form another 2nd order filter with R1 = 10*R2 and C2 = C4/10. The two similar points in this filter should also be plotted, the output of the first section at node dB-3 and the output of the second section at node dB-4. This second filter keeps the RC time constant the same for both sections of the filter but reduces the loading effect by increasing the value of the second resistor by a factor of 10 and decreases the value of the second capacitor by a similar factor of 10 (keeping the RC product the same). Using a factor of 10 like this is a good rule of thumb to use when designing cascaded passive RC filters. |
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| Run the simulation sweeping the input frequency from 100 Hz to 20 KHz. You should get a frequency response plot the looks something like figure 2. | Run the simulation sweeping the input frequency from 100 Hz to 20 KHz. You should get a frequency response plot the looks something like figure 2. |
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| {{ :university:courses:alm1k:circuits1:alm-cascade-rc-f1.png?350 |}} | {{ :university:courses:alm1k:circuits1:cascade_rc_sch.png?400 |}} |
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| <WRAP centeralign>Figure 1 ADIsimPE schematic of RC filters</WRAP> | <WRAP centeralign>Figure 1 Simulation schematic of RC filters</WRAP> |
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| A simulation was run sweeping the frequency from 100 Hz to 20 KHz. As we can see in figure 2 the completely unloaded 1st order filter (dB-0 green line) and the lightly loaded 1st order point (dB-3 slightly darker green line) are nearly on top of each other. The loaded 1st order point (dB-1 olive line) is significantly lower than the other two lines at the frequency of the RC time constant. However, all three converge to the same point at high frequencies, 20 KHz. The two 2nd order output points at dB-2 (blue line, loaded) and dB-4 (red line, lightly loaded) also show significant differences at the RC time constant frequency but also converge to the same point at 20 KHz. At 20 KHz the response of the 2nd order filters is 20 dB lower than the 1st order filters as one would expect. | A simulation was run sweeping the frequency from 100 Hz to 20 KHz. As we can see in figure 2 the completely unloaded 1st order filter (dB-0 green line) and the lightly loaded 1st order point (dB-3 slightly darker green line) are nearly on top of each other. The loaded 1st order point (dB-1 blue line) is significantly lower than the other two lines at the frequency of the RC time constant. However, all three converge to the same point at high frequencies, 20 KHz. The two 2nd order output points at dB-2 (red line, loaded) and dB-4 (pink line, lightly loaded) also show significant differences at the RC time constant frequency but also converge to the same point at 20 KHz. At 20 KHz the response of the 2nd order filters is 20 dB lower than the 1st order filters as one would expect. |
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| {{ :university:courses:alm1k:circuits1:alm-cascade-rc-f2.png?550 |}} | {{ :university:courses:alm1k:circuits1:cascade_rc_sim.png?600 |}} |
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| <WRAP centeralign>Figure 2 AC sweep simulation plot</WRAP> | <WRAP centeralign>Figure 2 AC sweep simulation plot</WRAP> |
| Are the two plots the same? If not explain any differences and why. You will want to again capture a screen shot of this plot to include in your lab report. | Are the two plots the same? If not explain any differences and why. You will want to again capture a screen shot of this plot to include in your lab report. |
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| As a way to better understand what is happening due to the changes to R<sub>2</sub> and C<sub>2</sub> move Channel B back to the top of C<sub>1</sub> and click the<sub></sub>green start button again. Compare this response curve to the one you observed at the top of C<sub>1</sub> when R<sub>2</sub> was 1 KΩ and C<sub>2</sub> was 0.1 uF. Explain any difference you observe and why. You will want to again capture a screen shot of this plot to include in your lab report. | As a way to better understand what is happening due to the changes to R<sub>2</sub> and C<sub>2</sub> move Channel B back to the top of C<sub>1</sub> and click the green start button again. Compare this response curve to the one you observed at the top of C<sub>1</sub> when R<sub>2</sub> was 1 KΩ and C<sub>2</sub> was 0.1 uF. Explain any difference you observe and why. You will want to again capture a screen shot of this plot to include in your lab report. |
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| **Third order filter** | **Third order filter** |
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| As a further extension of this cascade of RC low pass filter sections add a third RC section to make a 3rd order filter by connecting R<sub>3</sub> and C<sub>3</sub> to your circuit as shown in figure 5. Follow the same steps you just did on the 2nd order filter with R<sub>1</sub> = R<sub>2</sub> = R<sub>3</sub> and C<sub>1</sub> = C<sub>2</sub> = C<sub>3</sub>, and again with R<sub>1</sub> = 1KΩ, R<sub>2</sub> = 10KΩ, R<sub>3</sub> = 100KΩ and C<sub>1</sub> = 0.1uF, C<sub>2</sub> = 0.01uF, C<sub>3</sub> = 0.00uF. | As a further extension of this cascade of RC low pass filter sections add a third RC section to make a 3rd order filter by connecting R<sub>3</sub> and C<sub>3</sub> to your circuit as shown in figure 5. Follow the same steps you just did on the 2nd order filter with R<sub>1</sub> = R<sub>2</sub> = R<sub>3</sub> and C<sub>1</sub> = C<sub>2</sub> = C<sub>3</sub>, and again with R<sub>1</sub> = 1KΩ, R<sub>2</sub> = 10KΩ, R<sub>3</sub> = 100KΩ and C<sub>1</sub> = 0.1uF, C<sub>2</sub> = 0.01uF, C<sub>3</sub> = 0.001uF. |
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| Explain any differences you observe in the frequency responses and be sure to save screen shots along the way to include in your lab report. | Explain any differences you observe in the frequency responses and be sure to save screen shots along the way to include in your lab report. |
| {{ :university:courses:alm1k:circuits1:alm-cascade-rc-f5.png?600 |}} | {{ :university:courses:alm1k:circuits1:alm-cascade-rc-f5.png?600 |}} |
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| <WRAP centeralign>Figure 5 3rd order passive RC low pass filter</WRAP> | <WRAP centeralign>Figure 5. 3rd order passive RC low pass filter</WRAP> |
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| | {{ :university:courses:alm1k:circuits1:cascaded_rc_bb.png?400 |}} |
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| | <WRAP centeralign>Figure 6. 3rd order passive RC low pass filter breadboard connections</WRAP> |
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| One final question, how do your measured results compare to your simulation results (as in figure 2)? Explain any differences. | One final question, how do your measured results compare to your simulation results (as in figure 2)? Explain any differences. |
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| | **Resources:** |
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| | * Fritzing files: [[downgit>education_tools/tree/master/m1k/fritzing/cascaded_rc_bb |cascade_rc_bb]] |
| | * LTSpice files: [[downgit>education_tools/tree/master/m1k/ltspice/cascade_rc_ltspice | cascade_rc_ltspice]] |
| | * ADISimPE files: [[downgit>education_tools/tree/master/m1k/adisimpe/cascaded_rc_adisimpe | cascade_rc_adisimpe]] |
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| **For Further Reading:** | **For Further Reading:** |
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| [[http://www.analog.com/en/design-center/interactive-design-tools/adisimpe.html|ADIsimPE]] | [[adi>en/design-center/design-tools-and-calculators/ltspice-simulator.html|LTSpice]]\\ |
| | [[adi>en/design-center/interactive-design-tools/adisimpe.html|ADIsimPE]] |
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| **Return to Lab Activity [[university:courses:alm1k:alm_circuits_lab_outline|Table of Contents]]** | **Return to Lab Activity [[university:courses:alm1k:alm_circuits_lab_outline|Table of Contents]]** |
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