Receiver Noise Figure Calculation

Receiver Noise Figure Calculation:

It is defined as the measure of noise produced by a practical receiver compared to noise of an ideal receiver. The noise figure is expressed as,

F_n = N_out/KT_oB_nG

Where, N_out – available output noise power

K – Boltzmann’s constant

G – Gain

T_o – Standard temperature

B_n – noise bandwidth

If additional noise is introduced by practical network, then

Noise figure = F_n = (KT_oB_nG + ΔN)/ KT_oB_nG

F_n = 1+ ΔN/ KT_oB_nG

Noise Figure in Cascade Networks:

Consider two networks in cascade each with same noise and Bandwidth but with different gain. Let the noise from the first network be F₁KT₁B_nG₁G₂ and the noise from second network be (F₂-1) KT_oB_nG₂.

Therefore, the output noise, N_out = noise from first network + noise from second network

ie, N_out = F₁KT₁B_nG₁G₂ + (F₂-1) KT_oB_nG₂

Let, N_out = F_oKT₀B_nG₁G₂

Therefore the above equation becomes,

F_oKT_oB_nG₁G₂ = F₁KT₁B_nG₁G₂ + (F₂-1) KT_oB_nG₂

F_o = [F₁KT₁B_nG₁G₂ + (F₂-1) KT_oB_nG₂]/ KT_oB_nG₁G₂

provides two output frequencies that are sum and difference of two input frequencies.

ie, f_RF ± f_LO

The difference frequency f_RF - f_LO is the desired IF frequency. The sum frequency f_RF + f_LO is removed by filtering. The RF Signal frequency is greater than local oscillator frequency, the output IF frequency will be,

f_IF = f_RF - f_LO

This is known as derived frequency.

• If the RF Signal frequency is less than local oscillator frequency, then the output IF signal will be,

f_IF = f_LO - f_RF. This is called Image Frequency.

MIXERS:

a. Single Ended Mixer:

It uses a single diode. The LO signal is inserted through a directional coupler. A low pass filter following the diode allows the IF Signal to pass through it by rejecting high frequencies. The diode of the mixer can produce non linear called ‘spurious responses’ which are unwanted intermediate frequency components.

b. Balanced Mixer:

The balanced mixer can be considered as two single ended mixers in parallel and 180^o out of phase. The LO Signal is applied to one port and RF signal is applied to second port. The signals inserted at these two ports appear in the third port as Sum and fourth port as Difference. The IF signal is obtained by subtracting the output of the two diode mixers. A double balanced mixer utilises four diodes connected in ring or bridge to produce the IF Signal output.

c. Image Rejection Mixer:

In an image rejection mixer, the RF signal is split and fed to two mixers. The LO Signal is fed into one port of a 90^o hybrid junction that produces 90^o phase difference between the LO inputs to the two mixers. The IF hybrid junction provides another 90^o phase difference in such a manner, that signal frequency and image frequency are separated.