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Link Budget:

Definition:

A link budget is an accounting of all the gains and losses from the transmitter, through the medium (free space, cables, etc.), to the receiver in a communications system. It determines if the received signal is strong enough for reliable communication.

\[ P_{RX} = P_{TX} + G_{TX} + G_{RX} - L_{P} - L_{TX} - L_{RX} - L_{M} \]

Parameter Table

Symbol Name Description Units
\(P_{RX}\) Received Power Power at the receiver input dBm / dBW
\(P_{TX}\) Transmitted Power Power at the transmitter output dBm / dBW
\(G_{TX}\) Transmitter Antenna Gain Gain of transmitting antenna dBi
\(G_{RX}\) Receiver Antenna Gain Gain of receiving antenna dBi
\(L_{P}\) Path Loss Free space or other path loss dB
\(L_{TX}\) Transmitter Losses Losses before the transmit antenna (cables, etc.) dB
\(L_{RX}\) Receiver Losses Losses after the receive antenna (cables, etc.) dB
\(L_{M}\) Miscellaneous Losses Other losses (fade margin, polarization, etc.) dB

Key Points

  • All terms are in dB (logarithmic scale) for easy addition/subtraction.
  • Path loss is typically the largest single loss.
  • Link budget ensures that the received power \((P_{RX})\) exceeds the receiver sensitivity for reliable communication.

Receiver Sensitivity:

Definition:

Receiver Sensitivity is the minimum input signal power that a receiver can detect with acceptable quality (i.e., with a given bit error rate, SNR, or other performance metric).

\[ P_{sens} = -174 + 10 \log_{10}(B) + NF + SNR_{min} \]

Where:

  • \(P_{sens}\): Receiver Sensitivity (in dBm)
  • \(B\): Bandwidth (Hz)
  • \(\(NF\)\): Receiver Noise Figure (dB)
  • \(SNR_{min}\): Minimum required Signal-to-Noise Ratio (dB)

-174 dBm/Hz is the thermal noise power density at room temperature (\(kT\) at \(T=290\)K).

Parameter Table (Receiver Sensitivity)

Symbol Name Description Units
\(P_{sens}\) Receiver Sensitivity Minimum detectable power dBm
\(B\) Bandwidth Receiver bandwidth Hz
NF Noise Figure Receiver noise figure dB
\(SNR_{min}\) Minimum SNR Required For desired performance (e.g., BER) dB

Note: \(k\) (Boltzmann's constant) and \(T\) (Temperature) are already included in the -174 dBm/Hz term for standard calculations at room temperature.

Noise Figure and Noise Factor

Noise Figure (NF) quantifies how much additional noise a receiver or component adds to the signal, relative to an ideal (noise-free) system.

  • It describes the degradation of the Signal-to-Noise Ratio (SNR) as the signal passes through a device.
  • Lower NF means a better receiver (adds less noise).
  • Noise Factor (\(F\)) is the linear ratio (unitless):

$$ F = \frac{SNR_{in}}{SNR_{out}} $$ * Noise Figure (\(NF\)) is the decibel (dB) form of Noise Factor:

$$ NF = 10 \log_{10}(F) $$

Where:

  • \(NF\): Noise Figure (dB)
  • \(SNR_{in}\): Signal-to-Noise Ratio at the input
  • \(SNR_{out}\): Signal-to-Noise Ratio at the output

Parameter Table (Noise Figure & Noise Factor)

Term Symbol Definition Unit
Noise Figure \(NF\) \(NF = 10 \log_{10}(F)\) dB
Noise Factor \(F\) \(F = SNR_{in} / SNR_{out}\) Unitless
Input SNR \(SNR_{in}\) Signal-to-noise ratio at input dB
Output SNR \(SNR_{out}\) Signal-to-noise ratio at output dB

Key Points

  • NF and F both describe noise performance: NF (in dB) is more common in datasheets.
  • Lower NF/F means better receiver quality—less noise is added by the system.
  • NF is critical in receiver sensitivity calculations and overall link performance.

Multistage (Cascaded) Amplifier Noise Figure – Quick Reference

  • Friis Formula for Cascaded Noise:

  • For N amplifier stages in cascade:

    \[ F_{\text{total}} = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1 G_2} + \cdots + \frac{F_N - 1}{G_1 G_2 \cdots G_{N-1}} \]
    • \(F_i\): Noise factor (linear, not dB) of the i-th stage
    • \(G_i\): Power gain (linear, not dB) of the i-th stage

  • Key Points:

  • First stage dominates total noise performance—maximize its gain and minimize its noise figure for best results.

  • Later stages contribute less noise if early stage gains are high.

  • Always use linear values for noise and gain in the Friis equation.

  • Example Calculation:

  • Given three stages:

    • Noise figures: 3 dB, 5 dB, 7 dB
    • Gains: 10 dB, 8 dB

    • Step 1: Convert to linear:

    • \(F_1 = 10^{3/10} = 2\)

    • \(F_2 = 10^{5/10} = 3.16\)
    • \(F_3 = 10^{7/10} = 5.01\)
    • \(G_1 = 10^{10/10} = 10\)
    • \(G_2 = 10^{8/10} = 6.31\)

    • Step 2: Plug into Friis:

    • \(F_{\text{total}} = 2 + \frac{3.16 - 1}{10} + \frac{5.01 - 1}{10 \times 6.31} = 2 + 0.216 + 0.0635 = 2.28\)

    • Step 3: Back to dB:

    • \(NF_{\text{total}} = 10 \log_{10}(2.28) \approx 3.58\,\text{dB}\)

  • Summary Table:

Stage Noise Figure (dB) Noise Factor Gain (dB) Gain (linear)
1 3 2.00 10 10.00
2 5 3.16 8 6.31
3 7 5.01 – –

Key Tip:

  • Focus on minimizing the noise figure and maximizing the gain of the first stage in a cascaded amplifier chain for best overall system noise performance.

_Last updated: June 06, 2025