---
title: "Delay equalization and how it is done"
subject: "Filter Design"
chapter: 2
key: "semester_5/filter_design:delay-equalization-how"
source: https://www.bctengineer.com/q/semester_5/filter_design/delay-equalization-how
site: BCT Engineering
---

# Delay equalization and how it is done

Filter Design · Chapter 2: Approximation Methods

- Asked in: 2072 Chaitra, 5 marks; 2072 Kartik, 4 marks (asked 2 times)
- Video: [Equalization Network Synthesis](https://www.youtube.com/watch?v=mE8oA1v8tAA) — Keysight Design Software
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/filter_design/delay-equalization-how
- Whole chapter: https://www.bctengineer.com/md/semester_5/filter_design/chapter-2

## Question

What is delay equalization? How can it be done? Explain with necessary figures.

## Short answer

Delay equalization makes total group delay constant by cascading the filter with all-pass networks that add delay without changing magnitude. Total delay is the sum of filter and all-pass delays; first- and second-order all-pass sections are tuned to flatten the passband response.

## Answer

**Delay (phase) equalization** is the process of making the total group delay of a filter or channel nearly constant over the passband, by cascading it with all-pass networks.

Filters with a sharp magnitude response (Chebyshev, elliptic, high-order Butterworth) have a delay that peaks near the band edge, which distorts pulses and data signals. An all-pass section has $|T| = 1$, so it does not change the magnitude response, but it adds its own delay. The total delay is the sum:
$$
\tau_{total}(\omega) = \tau_{filter}(\omega) + \tau_{AP}(\omega)
$$
**How it is done:**
1. Plot or compute the delay $\tau_F(\omega)$ of the filter over the passband.
2. Choose first- and/or second-order all-pass sections whose delay is **large where $\tau_F$ is small** and small where $\tau_F$ is large (a second-order section gives a delay peak near its $\omega_o$, with height set by $Q$).
3. Adjust $a$, $\omega_o$ and $Q$ (and add sections) until $\tau_F + \tau_{AP}$ is flat within the allowed tolerance.
4. Realize the all-pass sections with op-amp circuits and cascade them with the filter.

```text
 tau      filter        equalizer        total
  |        .            .     .
  |      .' `.          `. .'         .------.
  | ...-'     `      ->   `     ->   '        `
  +----------- w      +------ w      +---------- w
```

**First-order op-amp all-pass:** two equal resistors $R_1$ in the inverting path and feedback, and an RC network at the + input, give $T(s) = \dfrac{1 - sRC}{1 + sRC}$.

```text
          R1        R1
 Vi o--+-/\/\-+---/\/\---+
       |      |  |\      |
       |      +--|-\     |
       R         |  >----+--o Vo
       |      +--|+/
       +------+  |/
              C
              |
             GND
```
Applications: data modems, telephone lines, video and pulse transmission, where waveform shape must be preserved.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is delay equalization?
   A. Making the total group delay nearly constant over the passband by cascading all-pass sections
   B. Equalizing the magnitude of ripple in the passband
   C. Reducing the stopband delay to zero
   D. Making input and output impedances equal
   Answer: A. All-pass networks add delay without changing magnitude. (Key point: Delay equalization)

2. Why do sharp filters need it?
   A. Their gain is below 0 dB
   B. They have too many poles
   C. Their delay peaks near the band edge, distorting pulses
   D. They have no phase
   Answer: C. Chebyshev, elliptic, and high-order Butterworth have delay peaks. (Key point: Why needed)

3. How should all-pass sections be chosen?
   A. Peak delay where the filter's delay already peaks
   B. Large delay where the filter's delay is small, small where it is large, so the sum is flat
   C. Delay equal to the filter's at all frequencies
   D. Delay only at dc
   Answer: B. τtotal = τfilter + τAP. (Key point: Choosing sections)

4. How do delays combine in a cascade?
   A. They add: τtotal = τfilter + τAP
   B. They multiply
   C. The larger one wins
   D. They subtract
   Answer: A. Phases add, so delays add. (Key point: Total delay)

## Close variants set in other exams

- [Delay and delay equalization](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Adelay-and-delay-equalization) — Filter Design, chapter 2, asked 3×

## Related in Filter Design

- [All-pass filters in delay equalization; 3rd order Bessel-Thomson](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Aallpass-importance-bessel-third-order) — Filter Design, chapter 2, asked 3×
- [All-pass in delay equalization; 4th order Bessel-Thomson](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Aallpass-bessel-fourth-order) — Filter Design, chapter 2, asked 3×
- [2nd order constant delay and delay equalization](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Aconstant-delay-second-order-equalization) — Filter Design, chapter 2, asked 2×
- [Delay equalization and its importance](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Adelay-equalization-importance) — Filter Design, chapter 2