EE539: Analog Integrated Circuit Design; Lecture 15

EE539: Analog Integrated Circuit Design; Lecture 15

Nagendra Krishnapura (nagendra@iitm.ac.in) 06 Feb. 2006

Input Referred noise

Noisy

Components S_v

out

Components Sv_out

Svin

V_in=0

Noiseless

Figure 1: Input Referred noise

Consider a network whose output noise power spectral density isS_vout. Now, if we make all the components in the network noiseless, then the noise that should be present at the input of the network in order to get the sameS_vout at the output is called the ”input referred noise”.

PSD of the input referred noise (Svin) is given by S_vin = ^Svout

|H(f)|² where|H(f)|is the transfer function from input to output.

Input referred noise is useful when we need to compare the noise and input signal level.

For e.g.Let us calculate the input referred noise for a MOSFET.(Fig. 2)

Sv_in = SI_D+SI_R

g_m² =

4kT

R +^8kTgm 3

g_m² = 4kT g_m

1 g_mR +2

3

Dynamic Range

Let us calculate the Dynamic Range of a MOSFET amplifier.

Let the input signal have a peak amplitudeV_p.Neglecting noise due to load resistance and assuming a band- width of B,

1

2

Vdd

R

S_ID=(8/3)KTg_m S_IR=4KT/R

Figure 2: MOSFET noise

S N

i

= _V

√p

2

q8kT B

3g_m

For an SNR of 0dB,

Vpmin = s

16kT B 3gm

For a max Harmonic Distortion of x%,

V_pmax Vpmin

= 4(VGS−V_T)x q16kT B

3g_m

= 4x q16kT B

3

rµCoxW

L (V_GS−V_T)³²

= V_pmax Vpmin

= 4x q16kT B

3

1 µC_oxW

L

¹₄(2ID)³⁴

Dynamic Range= 20∗log_V

pmax

V_pmin

From these equations, we see that the dynamic range can be increased by

• increasing the overdrive for the same aspect ratio

• decreasing the aspect ratio while keeping the bias current constant. (But it is a weak function of aspect ratio)

3

Common Drain Amplifier(Source Follower) Vdd

V

_in

V

_out

I

₀

Figure 3: Source Follower Consider the source follower (Fig. 3)

Vout =Vin +VGS=Vin +VT +

s 2I0

„

µCox^W

L

«

Small signal gain = 1 (if there is no body effect)