How may noise voltage and noise figure be compared?

Question

For instance, comparing the MIC920 and the BGA2818, it's expected that since the latter is intended for application as an RF LNA and the former is general-purpose, the BGA2818 would out-perform the MIC920 in RF applications. But how could this be proven?

The MIC920 specifies only an input noise voltage; let's assume they intended to write nV instead of V:

And the BGA2818 specifies only an input noise figure:

The "naive" comparison would be (following the Maxim App Note 2895):

BW for my application = 5 kHz

Gain of MIC920 ~ 85dB

Output power noise density: $$V_{IN} = \left( 11 \frac {\text {nV}} {\sqrt{\text {Hz}}} \right) \sqrt{5 \text{kHz}} = 778 \text {nV} $$ $$ P_{IN} = 10 \log \left( \frac {778 \text {nV}} {50 \Omega \cdot 10^{-3}} \right) = -48.1 \text{dBm} $$

$$P_{OUT} = -48.1 \text{dBm} + 85 \text{dB} = 36.9\text{dBm}$$

$$P_{NOUTD} = \frac {36.9\text{dBm}} {5\text{kHz}} = 7.38 \times 10^{-3} \frac {\text{dBm}} {\text{Hz}}$$

$$NF = 7.38 \times 10^{-3} \frac {\text{dBm}} {\text{Hz}} + 174 \frac {\text{dBm}} {\text{Hz}} - 85 \text{dB} = 89 \text{dB}$$

Is this calculation valid?

Answer 1

At 50 Ω, noise is \$\frac{E^2}{50} + I^2 \cdot 50 = -146\$ dBm/Hz; \$174-146= 27\$ dB noise figure at 50 Ω.

You don't need to consider the 5kHz, it cancels out. At low impedances, you can ignore In, at high impedances you can ignore \$V_n\$. (relative to equivalent noise resistance)

For an amplifier with \$V_n\$ and \$I_n\$ given, you can consider the equivalent noise resistance \$R_n = \frac{V_n}{I_n}\$.

This will be the impedance where noise figure will be lowest. In this case 15kohm.

As you see, it is very noisy at 50 Ω.

Noise power is \$V_nI_n=-171\$ dBm/Hz . Thermal noise is -174 dBm/Hz, so the noise figure would be 3dB at 15 kΩ.

The numbers are only valid at low frequencies, at high frequencies they are different, so you can't really compare.

Answer 2

Simple answer: noise figure requires you define an impedance for interfaces in/out of the circuit.

When designing for predictable noise floors on silicon, must a 50_ohm reference resistance be used? No. Why waste signal power into unneeded "Load resistors".

At times the Loads (or Source-located series-terminations Rs) are needed for stability, but that is a different issue.

At high frequencies in tiny systems (onchip) you often can approach the noise analysis as if you are designing high-speed opamps of near-zero size. In this case, you need not have well-defined interface impedances, unless as stated above there are peaking/oscillation/stability issues.