# Task 7.14: Manual Frequency Response Analysis >[!figures] Figure I: Low-Pass Filter Circuit Schematic >![[Pasted image 20260311224151.png|center|350]] >[!table] Table I: Measured Data for RL Low-Pass Filter Frequency Response > | Frequency [Hz] | $V_{out}$ [Vpp] | $V_{in}$ [Vpp] | Gain [dB] | | ---: | ---: | ---: | ---: | | 10 | 0.968278 | 1 | -0.28 | | 11.5 | 0.967164 | 1 | -0.29 | | 12.7 | 0.971628 | 1 | -0.25 | | 14.2 | 0.968278 | 1 | -0.28 | | 16.1 | 0.967164 | 1 | -0.29 | | 18.4 | 0.969393 | 1 | -0.27 | | 21.2 | 0.963829 | 1 | -0.32 | | 23.5 | 0.962720 | 1 | -0.33 | | 26.4 | 0.970510 | 1 | -0.26 | | 30.5 | 0.963829 | 1 | -0.32 | | 34.3 | 0.967164 | 1 | -0.29 | | 38.4 | 0.966051 | 1 | -0.30 | | 43.7 | 0.963829 | 1 | -0.32 | | 49.8 | 0.962720 | 1 | -0.33 | | 56.2 | 0.966051 | 1 | -0.30 | | 64.4 | 0.963829 | 1 | -0.32 | | 71.5 | 0.962720 | 1 | -0.33 | | 81.6 | 0.968278 | 1 | -0.28 | | 92.3 | 0.963829 | 1 | -0.32 | | 103.5 | 0.966051 | 1 | -0.30 | | 115.7 | 0.966051 | 1 | -0.30 | | 132.4 | 0.960506 | 1 | -0.35 | | 149.6 | 0.962720 | 1 | -0.33 | | 168.2 | 0.966051 | 1 | -0.30 | | 193.5 | 0.963829 | 1 | -0.32 | | 217.9 | 0.966051 | 1 | -0.30 | | 242.9 | 0.966051 | 1 | -0.30 | | 277.3 | 0.963829 | 1 | -0.32 | | 312.2 | 0.962720 | 1 | -0.33 | | 353.4 | 0.966051 | 1 | -0.30 | | 399.7 | 0.963829 | 1 | -0.32 | | 451.9 | 0.962720 | 1 | -0.33 | | 507.4 | 0.966051 | 1 | -0.30 | | 578.3 | 0.963829 | 1 | -0.32 | | 651.6 | 0.962720 | 1 | -0.33 | | 734.7 | 0.968278 | 1 | -0.30 | | 836.9 | 0.967164 | 1 | -0.32 | <div style="page-break-after: always;"></div> >[!figures] Figure II: RL Low-Pass Filter Frequency Response >![[Pasted image 20260311230526.png|center|500]] # Task 7.15: Exploring FRA on the Oscilloscope >[!figures] Figure III: RL Circuit Schematic (Low-Pass) >![[Pasted image 20260311224209.png|center|350]] <div style="page-break-after: always;"></div> >[!figures] Figure IV: Gain and Phase vs. Frequency for Low-Pass Filter >![[Pasted image 20260311224214.png|center|350]] >[!figures] Figure V: Gain vs. Frequency for Low-Pass Filter >![[Pasted image 20260311224221.png|center|350]] >[!calculation] Low-Pass Cutoff Frequency Percent Error > > $\text{Prelab cutoff frequency}=29\text{ kHz}$ > $\text{Measured cutoff frequency}=30.2\text{ kHz}$ > $\%\text{error}= \left|\frac{30.2-29}{29}\right|\cdot100=4.14\%$ > [!note] > The measured cutoff frequency was close to the prelab value, with a percent error of 4.14\%. The small discrepancy is mainly due to using a 180 $\Omega$ resistor instead of the calculated 183 $\Omega$, along with probe loading, wiring resistance, and connection quality on the breadboard. <div style="page-break-after: always;"></div> >[!figures] Figure VI: RL Circuit Schematic (High-Pass) >![[Pasted image 20260311224228.png|center|350]] >[!figures] Figure VII: Gain and Phase vs. Frequency for High-Pass Filter >![[Pasted image 20260311224235.png|center|350]] <div style="page-break-after: always;"></div> >[!figures] Figure VIII: Gain vs. Frequency for High-Pass Filter >![[Pasted image 20260311224241.png|center|350]] >[!calculation] High-Pass Cutoff Frequency Percent Error > > $\text{Prelab cutoff frequency}=9.947\text{ kHz}$ > $\text{Measured cutoff frequency}=10.96\text{ kHz}$ > $\%\text{error}= \left|\frac{10.96-9.947}{9.947}\right|\cdot100=10.18\%$ # Task 7.16: Variable Band Filter >[!figures] Figure IX: Band Filter Circuit Schematic >![[Pasted image 20260311224352.png|center|350]] >[!figures] Figure X:Gain and Phase Response of the Band-Pass Filter (config. 1) >![[Pasted image 20260311224404.png|center|350]] >[!figures] Figure XI: Gain and Phase Response of the Band-Pass Filter (config. 2) >![[Pasted image 20260311224410.png|center|350]] >[!calculation] Band-Pass Center Frequency Errors > > ##### 10 k$\Omega$ Bandwidth > $f_{0,\text{prelab}}=15{,}915\text{ Hz}$ > $f_{0,\text{measured}}=38{,}223\text{ Hz}$ > $\%\text{error}= \left|\frac{38{,}223-15{,}915}{15{,}915}\right|\cdot100=140.2\%$ > > ##### 0 $\Omega$ Bandwidth > $f_{0,\text{prelab}}=15{,}915\text{ Hz}$ > $f_{0,\text{measured}}=19{,}234\text{ Hz}$ > $\%\text{error}= \left|\frac{19{,}234-15{,}915}{15{,}915}\right|\cdot100=20.9\%$ >[!figures] Figure XII: Modified Band-Pass Filter Circuit w/ Additional Resistive Network. >![[Pasted image 20260311224609.png|center|350]] <div style="page-break-after: always;"></div> >[!figures] Figure XIII: FRA Gain/Phase Response of Modified Band-Pass Filter. >![[Pasted image 20260311224633.png|center|350]] >[!figures] Figure XIV: Measurement Showing how Modified Circuit Changes the Center Frequency and Bandwidth >![[Pasted image 20260311224642.png|center|350]] >[!calculation] Band-Reject Center Frequency Errors > > ##### 10 k$\Omega$ Bandwidth > $f_{0,\text{prelab}}=15{,}915\text{ Hz}$ > $f_{0,\text{measured}}=15{,}850\text{ Hz}$ > $\%\text{error}= \left|\frac{15{,}850-15{,}915}{15{,}915}\right|\cdot100=0.4\%$ > > ##### 0 $\Omega$ Bandwidth > $f_{0,\text{prelab}}=15{,}915\text{ Hz}$ > $f_{0,\text{measured}}=17{,}780\text{ Hz}$ > $\%\text{error}= \left|\frac{17{,}780-15{,}915}{15{,}915}\right|\cdot100=11.7\%$