# Engineering Notes

## RF POWER AMPLIFIERS TECHNICAL REFERENCE MATERIAL

### Noise Figure & Level

**Noise figure** is defined as:

NF = ((Si/Ni) Signal To Noise At Input (Source)) / ((So/No) Signal To Noise At Output)

BackgroundN = Noise Power = kTB Where K = Boltzman's Constant = 1.38 *10^{-23}Joules/Kelvin T = Absolute Temperature, K(0^{o}C = 273K) B = 3 dB Noise Bandwidth, Hz

**Example:** What is the noise level, in dBm, of a resistor (black body) at 17^{o}C (room temperature)
over a 1 MHz bandwidth?

N = kTB = (1.38 *10^{-23}) * (273 + 17) * (1 *10^{6})
= 1.37 *10^{-17} *290 = 4.0 *10^{-15} Joules/Second

Or = 4 *10^{-15} Joules/Second = 4 *10^{-15} Watts

**In dBm** 1 *10^{-15} Watts = 1 *10^{-12} mW = -120 dBm

Power Ratio of 4 = +6 dB

Noise level = -120 dBm + 6 dB = -114 dBm (Plot A on nomograph)

**Note:** NF of transistors are 2 dB to 30 dB due to bias currents, materials, etc.

**Noise Level** in dBm at the input of an amplifier assuming NF = 10 dB is - 104 dBm (Plot B):

**Noise Level** at the output, assuming the gain of the amplifier is 50 dB is:

No = KTB + NF + Gain = -114 dBm + 10 dB + 50 dB = -54 dBm

**Example:** If you add the gain of the amplifier to its NF (e.g., 50 dB + 10 dB = 60 dB),
plot C indicates -54 dBm output noise level.