Lecture 6

Higher Order Filters UsingInductor Emulation

Inductor Emulation Using Two-port Network

GIC (General Impedance Converter)

GII (General Impedance Inverter)

GyratorPositive Impedance Inverter

Floating inductor

Gyrator Example

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

Riordan Gyrator

Example

For Gyration resistance=1kΩ

Antoniou GIC

Antoniou GIC

Inductance emulation is optimum in case of no floating inductorsi.e., LC high-pass filters

Example

3rd Order LPF

6th 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 (ω0 , 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 nth order

• 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

2nV = Sv(f) = 4kTR, f 0,

where k = 1.3810 23 J/K is the Boltzmann constant and Sv(f) is expressed in V2/Hz.

Minimum signal (noise limited)

• Example: low-pass filter

We compute the transfer function from VR to Vout: 1

1

RCs

sVV

R

out

From the theorem, we have 14

14 2222

2

fCRkTRf

VVfSfSR

outRout

.

The total noise power at the output:

CkT

uuu

CkTdf

fCRkTRP outn

0tan2

144 1

0 2222, (V2)

Simple Example

Large R, Small C Large noise, parasitic sensitive

Large C, Small R Large power, large area