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Insertion gain/loss, design steps, active vs passive

Short answer

Insertion gain: 20 log|V2/V20|; insertion loss is its negative. Design steps: specifications, normalization, approximation, realization, denormalization, non-ideality study, construction. Active filters: op-amp based, provide gain, no inductors, limited bandwidth; passive filters: RLC, have insertion loss, handle high frequency and power.

What do you mean by insertion gain and insertion loss? Show the steps involved in the design filter. Compare active and passive filters.

Insertion gain and insertion loss

Insertion gain and insertion loss compare the load voltage with and without the filter between a source V1V_1 (resistance RsR_s) and load RLR_L.

 Without filter:  Rs                 With filter:  Rs   +--------+
  V1 o--/\/\--+-- RL  (V20)          V1 o--/\/\--| filter |-- RL (V2)
                                                 +--------+
V20=RLRs+RLV1,Insertion gain=20log⁡10∣V2V20∣ dBV_{20} = \frac{R_L}{R_s + R_L}V_1, \qquad \text{Insertion gain} = 20\log_{10}\left|\frac{V_2}{V_{20}}\right|\ \text{dB} Insertion loss=20log⁡10∣V20V2∣=−(insertion gain) dB\text{Insertion loss} = 20\log_{10}\left|\frac{V_{20}}{V_2}\right| = -(\text{insertion gain})\ \text{dB}

A passive filter normally has a positive insertion loss; an active filter can have insertion gain.

Steps in filter design

  1. Specifications: state the filter type (LP, HP, BP, BS) and αmax,αmin,ωp,ωs\alpha_{max}, \alpha_{min}, \omega_p, \omega_s, gain, impedance levels.
  2. Normalization: convert to a normalized low-pass prototype (ωp\omega_p = 1 rad/s, 1 Ω), using frequency transformation for HP/BP/BS.
  3. Approximation: choose a response (Butterworth, Chebyshev, inverse Chebyshev, elliptic, Bessel), find the order nn and the transfer function T(s)T(s) that meets the specifications.
  4. Realization (synthesis): build a circuit for T(s)T(s): a passive LC ladder, or cascaded active biquads (Sallen–Key, MFB, Tow–Thomas), or switched-capacitor sections.
  5. Denormalization (scaling): apply frequency and magnitude scaling (and the inverse frequency transformation) to get practical element values.
  6. Study of non-idealities: check sensitivity to element tolerances, op-amp limits and temperature; simulate.
  7. Construction and testing: build, measure and tune the filter.

Active vs passive filters

Active filterPassive filter
Uses R, C and op-amps (or transistors)Uses only R, L, C
Can give gain (> 0 dB)No gain; has insertion loss
No inductors needed; small, IC-friendlyInductors are large and heavy at low frequency
Needs a DC power supplyNo power supply
High input, low output impedance; easy cascadingLoading between stages
Limited by op-amp bandwidth (up to about MHz)Works up to hundreds of MHz/GHz
Limited signal swing, adds noiseHandles large power, low noise

✓ Answer checked by Claude Sonnet 5.5

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