---
title: "Short note: LNA cavity device / insertion loss"
subject: "RF and Microwave Engineering"
chapter: 6
key: "semester_7/rf_and_microwave_engineering:lna-insertion-loss-note"
source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/lna-insertion-loss-note
site: BCT Engineering
---

# Short note: LNA cavity device / insertion loss

RF and Microwave Engineering · Chapter 6: RF Design Practices

- Asked in: 2072 Asoj, 5 marks
- Video: [Design Steps for RF filter using Insertion Loss Method #RFDesign #Microwave #RFcircuit](https://www.youtube.com/watch?v=eV_d3_0MwU4) — We The Engineers
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/lna-insertion-loss-note
- Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-6

## Question

Write a short note on LNA cavity device inserting loss method for filter designing.

## Short answer

The insertion loss method designs filters from a specified power loss ratio PLR = 1/(1 − |Γ|²); choose Butterworth or Chebyshev response, find order N, read prototype g-values, then scale and transform and realise with high-Q cavity resonators. Low loss before an LNA is essential because filter insertion loss adds directly to the system noise figure.

## Answer

The question is read as a short note on the **insertion loss method of filter design**, as used for the cavity and other filters around a low-noise amplifier (LNA) front end.

**Insertion loss method:** the filter is synthesised from a chosen power loss ratio:

```text
PLR = 1/(1 − |Γ(ω)|²),   IL = 10 log PLR (dB)
Butterworth: PLR = 1 + k²(ω/ωc)^(2N)
Chebyshev:   PLR = 1 + k²·TN²(ω/ωc)
```

**Steps:**

1. Specify cut-off/band, ripple, stopband rejection and R0.
2. Choose the response and order N.
3. Take low-pass prototype values gk from tables.
4. Scale and transform (LP → BP for a receiver pre-select filter).
5. Realise with transmission lines, coupled lines, or **cavity resonators** (high Q), then tune.

**Why it matters for an LNA:** a band-pass filter is placed before or after the LNA to reject out-of-band interferers and image signals. Filter loss before the LNA adds directly to the system noise figure (NF_total ≈ IL_filter + NF_LNA in dB), so a low-loss, high-Q cavity filter is preferred at the input. The insertion loss method lets the designer choose the lowest order that meets the rejection need, keeping passband loss small.

| Response | Benefit | Cost |
|---|---|---|
| Butterworth | Flat passband | Slower roll-off |
| Chebyshev | Sharp roll-off | Passband ripple |

## Check yourself

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

1. How is the filter synthesised in the insertion loss method?
   A. From a chosen power loss ratio PLR = 1/(1 − |Γ|^2)
   B. From measured noise figure
   C. From cavity dimensions directly
   D. From image impedances
   Answer: A. The response is specified through PLR (Butterworth or Chebyshev) and the network is synthesised from it. (Key point: Insertion loss method)

2. Why is a low-loss filter preferred before the LNA?
   A. It raises the gain
   B. Its insertion loss adds directly to the system noise figure (NF_total ≈ IL + NF_LNA in dB)
   C. It lowers the LNA bias
   D. It removes the need for matching
   Answer: B. Loss ahead of the LNA degrades noise figure dB for dB, so a high-Q cavity filter with low loss is used. (Key point: Filter loss and noise figure)

3. Which statement about Butterworth and Chebyshev responses is correct?
   A. Butterworth has ripple, Chebyshev is flat
   B. Both have the same roll-off
   C. Chebyshev has no cost
   D. Butterworth has a flat passband but slower roll-off; Chebyshev rolls off sharply but has passband ripple
   Answer: D. Flatness is traded against steepness of the skirt. (Key point: Response trade-off)

## Related in RF and Microwave Engineering

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