How to Calculate RF Receiver Noise Figure: LNA Gain and Cascaded NF

An RF receiver can use a low-noise amplifier (LNA) with an excellent noise figure and still deliver disappointing sensitivity. The reason is that receiver noise figure depends on the complete signal chain, including losses before the LNA and the gain and noise of later stages.

This guide explains how to calculate cascaded noise figure using Friis' equation, evaluate LNA gain requirements, and understand how filters, mixers and IF amplifiers affect receiver sensitivity.

1. What Is RF Receiver Noise Figure?

Noise figure (NF) describes the degradation of signal-to-noise ratio (SNR) introduced by a receiver or RF component, referenced to a standard input noise temperature of 290 K.

Noise factor (F) is expressed as a linear ratio:

F = SNRin / SNRout

Noise figure converts the noise factor into decibels:

NF (dB) = 10 × log10(F)

To convert noise figure from dB into linear noise factor:

F = 10^(NF/10)

For example, an LNA specified with a 1.2 dB noise figure has a linear noise factor of approximately 1.318.

The noise figure of an entire receiver cannot be calculated by simply adding individual noise figures in dB. Engineers must consider the gain and noise factor of every stage.

2. Friis Equation for Cascaded Noise Figure

Friis' equation is widely used to calculate the overall noise factor of a cascaded RF receiver.

Ftotal = F1 + (F2 - 1)/G1 + (F3 - 1)/(G1 × G2) + (F4 - 1)/(G1 × G2 × G3) + ...

Where:

• Ftotal: Total receiver noise factor in linear form.

• F1, F2, F3: Linear noise factors of individual receiver stages.

• G1, G2, G3: Linear available power gains of preceding stages.

• G: Gain converted from dB using G = 10^(GdB/10).

After calculating the total noise factor, convert it back into decibels:

NFtotal = 10 × log10(Ftotal)

The key principle is that noise introduced by later stages is divided by the gain of preceding stages.

Therefore, the noise figure and gain of the first amplification stage are especially important in receiver design.

The conventional equation assumes a compatible noise definition, suitable stage matching and linear operation. In practical RF systems, impedance mismatch and frequency-conversion effects may require a more detailed analysis.

3. Practical Example: Calculating Cascaded Receiver Noise Figure

Consider a receiver consisting of four stages:

RF Filter → LNA → Frequency Converter → IF Amplifier

The following values are illustrative engineering assumptions, not specifications of particular manufacturer part numbers.

Step 1: Convert Noise Figure to Linear Noise Factor

Use:

F = 10^(NF/10)

For the LNA:

F2 = 10^(1.2/10) = 1.318

Apply the same conversion to the remaining receiver stages.

Step 2: Convert Gain from dB to Linear Values

Use:

G = 10^(Gain in dB / 10)

For example:

• RF filter: -1 dB = 0.794

• LNA: 20 dB = 100

• Frequency converter: -6 dB = 0.251

• IF amplifier: 15 dB = 31.623

Step 3: Apply Friis' Equation

Substitute the noise factors and linear gains:

Ftotal = 1.259 + (1.318 - 1)/0.794 + (3.981 - 1)/(0.794 × 100) + (2.512 - 1)/(0.794 × 100 × 0.251)

Ftotal ≈ 1.773

Step 4: Calculate Total Receiver Noise Figure

NFtotal = 10 × log10(1.773)

Overall Receiver Noise Figure ≈ 2.49 dB

Although the LNA itself has a noise figure of only 1.2 dB, the complete receiver has approximately 2.49 dB NF under these assumed conditions.

The insertion loss ahead of the LNA is a major contributor.

*Mixer note: The frequency-conversion stage in this example uses an assumed effective two-port noise figure. Actual mixers require consistent single-sideband (SSB) or double-sideband (DSB) noise conventions and appropriate treatment of image-frequency noise. Conversion loss must not automatically be treated as an equivalent mixer noise figure.

4. Why RF Loss Before the LNA Matters

Loss before the first low-noise amplifier can significantly degrade receiver sensitivity.

Typical sources of front-end loss include:

• RF bandpass filters

• Coaxial connectors and cables

• RF switches

• Duplexers and limiters

• PCB transmission lines

At the standard 290 K reference temperature, a passive matched component with 1 dB insertion loss has approximately 1 dB noise figure.

When this loss occurs before the LNA, the received signal is attenuated before low-noise amplification.

For comparison, moving the same idealized filter after the 20 dB LNA in the preceding example reduces the calculated receiver NF to approximately 1.57 dB, assuming the other stage characteristics remain unchanged.

However, placing the LNA before the filter is not always practical. RF preselection filters may be necessary to reject strong interfering signals and prevent LNA compression.

Engineers must balance receiver sensitivity, interference rejection and linearity.

5. How Much LNA Gain Is Required?

The LNA provides two important functions:

• Amplifying weak RF signals while introducing minimal additional noise.

• Reducing the input-referred noise contribution of downstream receiver stages.

Consider a simplified two-stage receiver:

• LNA gain: 20 dB

• LNA noise figure: 1.2 dB

• Downstream receiver noise figure: 8 dB

The linear values are:

G1 = 100

F1 = 1.318

F2 = 6.310

Applying Friis' equation:

Ftotal = 1.318 + (6.310 - 1)/100

Ftotal ≈ 1.371

Cascaded Noise Figure ≈ 1.37 dB

This illustrates how sufficient LNA gain suppresses the noise contribution of later stages.

However, excessive gain can create other problems, including:

• Receiver compression

• Intermodulation distortion

• ADC input overload

• Reduced receiver dynamic range

• Sensitivity to strong adjacent-channel signals

Therefore, engineers should evaluate LNA gain together with P1dB, IP3, input power limits and downstream receiver requirements.

6. How to Estimate RF Receiver Sensitivity

Receiver sensitivity is closely related to noise figure, bandwidth and the signal-to-noise ratio required for successful demodulation.

At approximately 290 K, the thermal noise density is:

-174 dBm/Hz

A first-order receiver noise-floor estimate is:

Noise Floor (dBm) ≈ -174 + 10 × log10(B) + NF

Where:

• B = Equivalent noise bandwidth in Hz

• NF = Overall receiver noise figure in dB

For example, assume:

• Receiver bandwidth: 1 MHz

• Receiver noise figure: 2.49 dB

• Required demodulator SNR: 10 dB

Noise Floor = -174 + 60 + 2.49

Noise Floor ≈ -111.51 dBm

Estimated sensitivity threshold:

-111.51 + 10 = -101.51 dBm

Estimated Receiver Sensitivity ≈ -101.51 dBm

This is an idealized thermal-noise estimate. Actual receiver sensitivity depends on modulation, error-rate requirements, implementation loss, antenna noise temperature and interference conditions.

7. Important Parameters When Selecting an RF LNA

When selecting an LNA, engineers should evaluate more than noise figure alone.

For applications involving very weak signals, such as satellite receivers, microwave instrumentation and sensitive RF front ends, low noise figure is especially important.

For systems exposed to strong interfering signals, dynamic range and linearity may be equally important.

8. Related LNA Products and Selection Resources

After completing the receiver noise budget, engineers can select suitable LNA families based on frequency range, gain, noise figure, linearity and integration requirements.

UMS Low Noise Amplifiers

UMS offers GaAs MMIC amplifier solutions for RF and microwave applications.

Read our existing guide: UMS LNA Amplifiers: RF Low Noise Amplifiers from 2GHz to 70GHz.

Narda-MITEQ Low Noise Amplifiers

Narda-MITEQ provides low-noise amplifier products for RF and microwave receiver applications.

Learn more: Narda-MITEQ Low Noise Amplifier Selection Guide.

Cryogenic Low Noise Amplifiers

Cryogenic LNAs are used in specialized low-temperature receiving systems where noise performance is critical.

See our guide: Narda-MITEQ Cryogenic LNA Selection Guide.

9. RF LNA Selection and RFQ Support

Calculating the receiver noise figure is an important step in selecting a suitable RF low-noise amplifier.

Before requesting an LNA quotation, prepare the following information:

• Operating frequency range

• Maximum allowable noise figure

• Required amplifier gain

• Input power and linearity requirements

• Power supply and bias conditions

• Package and operating temperature

• Manufacturer part number

• Required quantity and delivery schedule

Looking for an RF LNA or microwave amplifier?

DataStorageIC supports component sourcing and RFQ inquiries for RF and microwave applications.

Contact DataStorageIC with your part number and technical requirements to discuss product availability, pricing and lead time.