--- title: "Active vs passive; non-inverting (s+8)/(s+2)" subject: "Filter Design" chapter: 6 key: "semester_5/filter_design:active-passive-difference-noninverting" source: https://www.bctengineer.com/q/semester_5/filter_design/active-passive-difference-noninverting site: BCT Engineering --- # Active vs passive; non-inverting (s+8)/(s+2) Filter Design · Chapter 6: Active Filters - Asked in: 2076 Asoj, 4+3 marks - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/filter_design/active-passive-difference-noninverting - Whole chapter: https://www.bctengineer.com/md/semester_5/filter_design/chapter-6 ## Question What are the differences between active and passive filter? Design an active filter using non-inverting op-amp configuration with following transfer function. T(s) = (s+8)/(s+2) ## Short answer Active filters use op-amps, require power, can provide gain >1, and avoid inductors; passive filters use only R, L, C with gain ≤1. For T(s)=(s+8)/(s+2) using the non-inverting topology: R1=16.67 kΩ, R2=50 kΩ, C2=10 µF (DC gain 4, HF gain 1). ## Answer #### Differences between active and passive filters | Point | Active filter | Passive filter | |---|---|---| | Elements | R, C and op-amps/transistors | R, L, C only | | Inductors | Not needed | Needed (bulky at low f) | | Gain | Can be > 1 | Always ≤ 1 (loss) | | Power supply | Required | Not required | | Loading | Op-amp buffers; easy cascading | Stages load each other | | Frequency range | Limited by op-amp bandwidth (up to ~MHz) | Works up to very high (RF) frequencies | | Signal level | Limited by supply (saturation) | Handles large voltage/current | | Noise | Op-amp adds noise | Low noise (only R noise) | | Size/IC | Small, can be integrated | Large; inductors cannot be integrated | | Sensitivity | Often higher | Low (doubly terminated ladders) | #### Design of $T(s) = (s+8)/(s+2)$ **Non-inverting configuration:** $Z_1$ from the inverting input to ground, $Z_2$ from output to inverting input: $$ T(s) = 1 + \frac{Z_2}{Z_1} $$ Zero 8 > pole 2, high-frequency gain 1, DC gain 4. Use $Z_1 = R_1$, $Z_2 = R_2 \parallel C_2$: $$ T(s) = 1 + \frac{R_2}{R_1(1 + sR_2C_2)} = \frac{s + \frac{1}{R_2C_2}\left(1+\frac{R_2}{R_1}\right)}{s + \frac{1}{R_2C_2}} $$ ```text +---R2---+ | | +---||---+ | C2 | +------+-|-\ | | | >---+---- Vo R1 Vin---|+/ | GND ``` **Matching:** $\dfrac{1}{R_2C_2} = 2$ and $1 + \dfrac{R_2}{R_1} = \dfrac{8}{2} = 4$, so $R_2 = 3R_1$. Normalized: $C_2 = 1$ F, $R_2 = 0.5\ \Omega$, $R_1 = 0.1667\ \Omega$. With $C_2 = 10\ \mu$F: $R_2 = 50\ \text{k}\Omega$, $R_1 = 16.67\ \text{k}\Omega$. **Answer:** $R_1 = 16.67\ \text{k}\Omega$, $R_2 = 50\ \text{k}\Omega$, $C_2 = 10\ \mu$F (DC gain 4, HF gain 1). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How do active and passive filter gains compare? A. Both can exceed 1 B. Passive can exceed 1 C. Active can exceed 1; passive is always <= 1 D. Both always <= 1 Answer: C. Passive filters only lose signal. (Key point: Gain) 2. Which statement is correct? A. Active works to RF; passive only audio B. Both limited to 1 kHz C. Passive limited by op-amp D. Active limited by op-amp bandwidth; passive works up to RF Answer: D. Op-amp bandwidth limits active filters. (Key point: Frequency range) 3. For (s+8)/(s+2), DC and HF gains are: A. DC 4, HF 1 B. DC 1, HF 4 C. DC 8, HF 2 D. DC 4, HF 4 Answer: A. T(0) = 8/2 and T(inf) = 1. (Key point: DC and HF gain) 4. With C2 = 10 uF, R2 and R1 are: A. R2 = 16.67 kΩ, R1 = 50 kΩ B. R2 = 50 kΩ, R1 = 16.67 kΩ C. R2 = 5 kΩ, R1 = 1.67 kΩ D. R2 = R1 = 50 kΩ Answer: B. R2 = 1/(2×10^-5) = 50 kΩ; R1 = R2/3. (Key point: Values) ## Close variants set in other exams - [Non-inverting realization of (s+8)/(s+2)](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Anoninverting-realize-s-plus-8) — Filter Design, chapter 6, asked 5× - [Active filter; non-inverting (s+8)/(s+2)](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Aactive-filter-noninverting-s-plus-8) — Filter Design, chapter 6, asked 5× - [Active vs passive; realize 4(s+2)/(s+1)](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Aactive-passive-noninverting-4s-plus-2) — Filter Design, chapter 6, asked 5× ## Related in Filter Design - [Non-inverting filter: zero at 8, pole at 4, gain 2](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Anoninverting-zero-8-pole-4) — Filter Design, chapter 6, asked 2× - [Active filter advantages; bilinear zero 800, pole 400](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Aactive-advantages-bilinear-800-400) — Filter Design, chapter 6 - [Insertion gain/loss, design steps, active vs passive](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Ainsertion-loss-steps-active-passive) — Filter Design, chapter 1 - [Non-inverting realization of 4(s+200)/(s+100)](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Anoninverting-realize-4-s-plus-200) — Filter Design, chapter 6, asked 4× - [Non-inverting: zero at -4, pole at -8, HF gain 2](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Anoninverting-zero-4-pole-8) — Filter Design, chapter 6, asked 4× - [Non-inverting: zero at -5, pole at -3, HF gain 2](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Anoninverting-zero-5-pole-3) — Filter Design, chapter 6, asked 3× ## Related in other subjects - [Non-inverting op-amp voltage gain](https://www.bctengineer.com/question.md?key=semester_1%2Ffundamental_of_electrical_and_electronics_engineering%3Anon-inverting-amplifier-gain) — Fundamental of Electrical and Electronics Engineering, chapter 6 - [Transfer function of op-amp phase-shift circuit](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-opamp-allpass-r1-c-r2) — Control Systems, chapter 2, asked 2× - [Transfer function of op-amp with Rs ∥ C feedback](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-opamp-rs-c-r1-r2) — Control Systems, chapter 2 - [Ideal op-amp properties; non-inverting gain](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-noninverting-gain) — Basic Electronics Engineering, chapter 4, asked 3×