Lecture 6

Higher Order Filters Using Inductor Emulation

Inductor Emulation Using Two-port Network GIC (General Impedance Converter) GII (General Impedance Inverter)

Gyrator Positive Impedance Inverter Floating inductor

Gyrator Example Gyration resistance=1/g1=1/g2=R

Riordan Gyrator

Example For Gyration resistance=1k Ω

Antoniou GIC

Antoniou GIC Inductance emulation is optimum in case of no floating inductors i.e., LC high-pass filters

Example 3 rd Order LPF 6 th Order BPF

Bruton’s transformation

FDNR Bruton’s inductor simulation based on FDNR Most suitable for LC LPF with minimum cap realization

Filter Performance & Design Trade-offs  Transfer function ( ω 0 , Q or BW, Gain, out-of-band attenuation, etc.)  Sensitivity (component variations, parasitics)  Dynamic range (DR) Maximum input signal (linearity) Minimum input signal (noise)  Power dissipation & Area

Maximum signal (supply limited)

Voltage swing scaling

Power dissipation For n th order

Minimum signal (noise limited) • Thermal noise of a resistor The thermal noise of a resistor

R

can be modeled by a series voltage source, with the one-sided spectral density

V n

2 =

S v

(

f

) = 4

kTR

,

f

 0, where

k

= 1.38

 10  23 J/K is the Boltzmann constant and

S v

(

f

) is expressed in V 2 /Hz.

• Example: low-pass filter We compute the transfer function from

V R

to

V out

:

V out V R

From the theorem, we have

S out



S R V out V R

 1

RCs

 1 2  1 4

kTR

4  2

R

2

C

2

f

2  1 . The total noise power at the output:

P n

,

out

  0  4

kTR

4  2

R

2

C

2

f

2  1

df

 2

kT



C

tan  1

u u u

   0 

kT

(V 2 )

C

Simple Example Large C, Small R Large R, Small C Large power, large area Large noise, parasitic sensitive