--- title: "Techniques for higher order active filters" subject: "Filter Design" chapter: 8 key: "semester_5/filter_design:higher-order-active-techniques" source: https://www.bctengineer.com/q/semester_5/filter_design/higher-order-active-techniques site: BCT Engineering --- # Techniques for higher order active filters Filter Design · Chapter 8: Design of High-Order Active Filters - Asked in: 2070 Asar, 4 marks - Video: [ECE 3306 Higher Order Cascaded Filters](https://www.youtube.com/watch?v=Ahdy1nsv_JQ) — Mary Baker - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/filter_design/higher-order-active-techniques - Whole chapter: https://www.bctengineer.com/md/semester_5/filter_design/chapter-8 ## Question What are the different techniques of designing higher order active filters? Discuss briefly. ## Short answer Cascade of second-order sections; direct simulation of passive LC ladders using gyrators, GICs, or FDNRs; operational simulation (leapfrog) based on state equations; and multiple-loop feedback topologies such as follow-the-leader feedback and primary-resonator blocks. ## Answer Higher-order active filters (order > 2) are designed by one of these methods: #### 1. Cascade design The transfer function is factored into second-order sections (plus one first-order section for odd order), each realised by a biquad (Sallen–Key, MFB, Tow–Thomas, KHN) and connected in cascade. Op-amp outputs have low impedance, so sections do not load each other. - Simple to design and tune; each pole pair is set separately. - Sensitivity is higher, especially for high-Q sections. - Order of sections: usually low Q first, high Q last. #### 2. Direct (element) simulation of the LC ladder Start from the doubly terminated LC ladder, which has the lowest sensitivity, and replace the inductors: - **Gyrator / GIC inductor simulation**: grounded inductors (highpass ladders) by GICs, floating ones by two GICs or gyrators. - **FDNR (Bruton transformation)**: divide impedances by $s$; inductors become resistors and capacitors become grounded FDNRs (lowpass ladders). #### 3. Operational simulation (leapfrog) The state equations of the ladder (currents and voltages of L and C) are realised with integrators and summers that feed each other alternately. It keeps the ladder's low sensitivity and suits lowpass and bandpass filters. #### 4. Multiple-loop feedback (MLF) Integrator or biquad blocks with several feedback paths, e.g. **follow-the-leader feedback (FLF)** and **primary-resonator block (PRB)**; the leapfrog is also a multiple-loop structure. | Method | Sensitivity | Ease of design/tuning | |---|---|---| | Cascade | higher | easiest | | Ladder simulation (GIC, FDNR) | low | moderate | | Leapfrog / MLF | low | more complex | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why can biquad sections be simply cascaded without loading each other? A. Their capacitors are equal B. Op-amp outputs have low impedance C. They share the same resistors D. They use different power supplies Answer: B. The low output impedance of an op-amp isolates each section from the next, so each pole pair can be set separately. (Key point: Cascade design) 2. What is the main drawback of the cascade method compared with ladder simulation? A. It cannot realise odd orders B. It needs inductors C. It is harder to tune D. Higher sensitivity, especially for high-Q sections Answer: D. Cascade is easiest to design and tune but has higher sensitivity than ladder-based methods. (Key point: Cascade drawback) 3. In the Bruton (FDNR) transformation of a lowpass LC ladder, what happens to the elements? A. Impedances are divided by s: inductors become resistors and capacitors become grounded FDNRs B. Inductors become capacitors and capacitors become inductors C. All resistors are removed D. Impedances are multiplied by s so inductors become capacitors Answer: A. Dividing every impedance by s turns inductors into resistors and capacitors into FDNRs, so no inductors are needed. (Key point: FDNR (Bruton) transformation) 4. What does the operational simulation (leapfrog) method realise? A. Each pole pair as a separate biquad B. The ladder's state equations using integrators and summers C. Inductors using gyrators D. A switched capacitor clock Answer: B. Leapfrog implements the ladder's L and C state equations with integrators and summers, keeping low sensitivity. 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