# Active Filters by goldessy

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```									Drexel University Electrical and Computer Engineering Dept. Advanced Analog Electronics, ECE-E421

TITLE: Active Filters

NAMES: Curtis King Salah Abushariefeh SECTION: 061 DATE PERFORMED: November 14, 2007 DATE DUE: November 28, 2007

Abstract: This lab exercise consists of comparing between calculated and designed three types of active filters and one cascaded filter. The filter types are as follow: 1- High pass filter implemented with a single feedback operational amplifier configuration. 2- Band pass filter implemented with a multiple feedback operational amplifier configuration. (Delyiannis-Friend Circuit) 3- Low pass filter implemented with a controlled-source configuration. (Sallen and Key Circuit) 4- Cascaded band pass filter with two identical filter stages of the single feedback, operational amplifier configuration.

Part I. Filter transfer function calculations: I. H(s) = Vo(s) / V1(s) = Ho*s^2 / ( s^2 + 2*ξ*ωn*s + ωn^2 )  high pass ξ = 0.5, fn = 250 Hz, ωn = 2*π*fn H(s) = Vo(s) / V1(s) = (C2 / C1)*s^2/(s^2 + (2/C1*R1 + 1/C2R1)*s + 1/R1*R2*C1*C2) H(s) = (10*s^2)/(s^2 + 1654.8*s + 2432.2*10^3)  Transfer function II. H(s) = Vo(s) / V1(s) = Ho*2*ξ*ωn *s / ( s^2 + ξ*ωn*s + ωn^2 )  low pass Ho = 4 V/V, ξ = 0.25, fn = 800 Hz, ωn = 2*π*fn H(s) = (10.1*10^3*s)/(s^2 + 2525.3*s + 25508*10^3)  Transfer function III. H(s) = Vo(s) / V1(s) = Ho*ωn^2 / ( s^2 + 2*ξ*ωn*s + ωn^2 )  band pass Ho = 2 V/V, ξ = 0.5, fn = 400 Hz, ωn = 2*π*fn H(s) = (12.63*10^6)/(s^2 + 2.5131*10^3*s + 6.3165*10^6)  Transfer function IV. H(s) = Vo(s) / V1(s) = Ho* s / ( s + ωp1)(s + ωp2)  cascaded band pass

Ho = 1 V/V, ωp1 = 1000 / 2*π = 159.2 Hz, ωp2 = 20000/ 2*π = 3184.7 Hz H(s) = s / (s + 160) (s + 3185)  Transfer function

Part II: Circuit diagrams:

Figure 1. High pass filter circuit diagram that uses uA741 op-amp.

Figure 2. Cascaded band pass filter circuit diagram that uses two uA741 op-amp.

Figure 3. Band pass filter circuit diagram that uses uA741 op-amp

Figure 4. Low pass filter circuit diagram that uses uA741 op-amp

PartIII: Graphs.

Figure 5. Equivalent high pass filter characteristics using MATLAB.

Figure 6. Equivalent band pass filter characteristics using MATLAB.

Figure 7. Equivalent low pass filter characteristics using MATLAB.

Figure 8. High pass filter characteristics using LabView frequency response.

Figure 9. Band pass filter characteristics using LabView frequency response.

Figure 10. Low pass filter characteristics using LabView frequency response.

Figure 11. Cascaded band pass filter characteristics using LabView frequency response.

Filter Type Highpass Bandpass Lowpass Cascaded bandpass fn fn fn fp1 fp2 Expected, Hz 250 800 400 159.2 3184.2 Measured, Hz 260 905 385 175 2850 %error 4 13.125 3.75 9.92462 10.49557

Table 1. Summery of the filter frequencies based on the frequency curved and preparations.

Conclusion: As expected, the frequencies obtained from the simulation are definitely different from the calculated ones. However, the error margin for all of them is less than eleven percent as shown in table on. Theses variations are caused by the capacitance and resistance of the circuit and/or those of the equipment. To produce more accurate results, the values of the capacitors need to be varied accordingly.

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