Post on 11-Aug-2015
description
Linear Integrated Circuits
Unit-III
Analog Multiplier and PLL
Multiplier Non linear operation Output proportional to the product of two signals Uses log and antilog circuits Applications
Frequency doubling, measurement of real power, detecting phase angle, multiplication, division, squaring a signal and square root of a signal
Single quadrant, two quadrant, four quadrant multiplier
Xx
y
xy / vref
Terminologies Accuracy: deriving actual output from ideal output Linearity: maximum percentage derivation from the
ideal output Linearity error: maximum absolute derivation,
imposes lower limit on accuracy Squaring mode accuracy: maximum derivation from
absolute square law curve Bandwidth: 3-dB Bw => output reduces by 3dB, Transconductance BW: transcon reduced by 3dB
Linear Error
Squaring Error
Analog multiplier using Emitter coupled transistor
Gilbert Multiplier cell
Gilbert Multiplier cell (DC Analysis)
Applications of Gilbert multiplier cell If V1 and V2 < VT Gilbert cell behaves as a
multiplier as tanh function becomes linear however, inclusion of non linearity can extend the input voltage range
One of the input is >VT the transistor associated with that behaves as switch; works as a modulator
Both inputs > VT all transistors behave as non saturating switches; useful in detection of phase difference between signals
Gilbert cell as a Multiplier
Pre-warping circuit – Inverse tanh
Continued… Differential o/p current is proportional to the product of
input voltages This holds good for output currents of differential voltage
to current convertors are positive Compensating non-linearity on V2 makes collector
current of Q1 and Q2 directly proportional to V2 rather than its tanh
Hence combination of Q1 and Q2 is redundant, output current of voltage-current converter can be fed to Q3-Q4, Q5-Q6 pairs
A Complete Analog Multiplier
Continued.. Complete analog multiplier consists of core transistors,
input voltage-current converters and output current to voltage amplifier
Core configuration is common to most four quadrant transconductance multipliers
The circuit has the transresistance The output voltage usually chosen so that And all the voltages have a ±10V range.
Variable Transconductance techniques The differential output of the basic
transconductance multiplier is Where is the transconductance Second input Vy applied w.r.t current source
can vary transconductance If then The overall output voltage is
It depends on absolute termeratureT It has a drawback, common mode voltage
swing caused being emitter current as a function of second input
Continued… This is overcome by using two differential stages in
parallel and cross coupling their output – Gilbert However the dynamic range is limited for linear multiplier
applications Features:
Simpler to integrate into a monolithic chip Cheaper, has good accuracy with reduced error It is available in four quadrant unlike logarithmic multiplier Available with high speed of operation Bandwidth of 10MHz an higher values are available
Generation of Logarithmic bias input for differential stage The voltage current transfer
characteristics of differential pair