01 signals and amplifiers

7/28/2019 01 Signals and Amplifiers

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Chapter 1Signals and Amplifiers

Lecture adopted from:Microelectronic Circuits (Sedraand Smith)Microelectronic Circuit Design (Jaeger and

Blalock)

By: August AlloUTSA (2011)

(Slides contain a combination of the text book figures, modifiedfiguresand slides, and slides added by August Allo to meet the instructors

preference and needs)

1

Chapter Goals

Explore the history of electronics.

Quantify the impact of integrated circuittechnologies.

Describe classification of electronic signals.

Review circuit notation and theory.

Introduce tolerance impacts and analysis.

Describe problem solving approach

2


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The Start of the Modern Electronics Era

Bardeen, Shockley, and Brattain atBell Labs - Brattain and Bardeen

invented the bipolar transistor in 1947.

The first germanium bipolartransistor. Roughly 50 years later,

electronics account for 10% (4 trilliondollars) of the world GDP.

3

Chap 1 - 4

Evolution of Electronic Devices

VacuumTubes

DiscreteTransistors

SSI and MSIIntegratedCircuits

VLSISurface-Mount

Circuits


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Chap 1 - 5

Microelectronics Proliferation

The integrated circuit was invented in 1958. World transistor production has more than doubled every

year for the past twenty years.

Every year, more transistors are produced than in allprevious years combined.

Approximately 1018 transistors were produced in a recentyear.

Roughly 50 transistors for every ant in the world.

*Source: Gordon Moores Plenary address at the 2003 International SolidState Circuits Conference.

Chap 1 - 6

Device Feature Size

Feature size reductionsenabled by processinnovations.

Smaller features lead tomore transistors per unitarea and therefore higherdensity.


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Chap 1 - 7

Rapid Increase in Density ofMicroelectronics

Memory chip densityversus time.

Microprocessor complexityversus time.

Chap 1 - 8

Signal Types

Analog signals take oncontinuous values -typically current orvoltage.

Digital signals appear atdiscrete levels. Usuallywe use binary signals

which utilize only twolevels.

One level is referred to aslogical 1 and logical 0 isassigned to the otherlevel.


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Chap 1 - 9

Analog and Digital Signals

Analog signals arecontinuous in time andvoltage or current.

(Charge can also be usedas a signal conveyor.)

After digitization, thecontinuous analog signalbecomes a set of discrete

values, typicallyseparated by fixed timeintervals.

Chap 1 - 10

Analog-to-Digital (A/D) Conversion

Analog input voltage vx is converted to the nearest n-bit number.

For a three bit converter, 0 to vx input yields a 000 ->111 digitaloutput.

Output is approximation of input due to the limited resolution of the n-bit output. Therefore, error is introduced.


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Chap 1 - 11

A/D Converter Transfer Characteristic

Chap 1 - 12

Digital-to-Analog (D/A) Conversion

Converts an n-bit digital input into an analog outputvoltage.


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Chap 1 - 13

Total signal =DC bias +time varying signal

Resistance and conductance - R and G with same subscripts willdenote reciprocal quantities. Most convenient form will be usedwithin expressions.

sigDCC

sigDCC

iIi

vVv

+=

+=

Gx =1

Rx and g

=

1

r

Notational Conventions

Chap 1 - 14

What are Reasonable Numbers?

If the power suppy is +-10 V, a calculated DC value of 15 V (notwithin the range of the power supply voltages) is unreasonable.

Peak-to-peak ac voltages should be within the power supply voltagerange.

A calculated component value that is unrealistic should be rechecked.For example, a resistance equal to 0.013 ohms or 1k farad capacitor.

Given the inherent variations in most electronic components, threesignificant digits are adequate for representation of results.


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Chap 1 - 15

Frequency Spectrum of ElectronicSignals

Non repetitive signals have continuous spectraoften occupying a broad range of frequencies

Fourier theory tells us that repetitive signals arecomposed of a set of sinusoidal signals withdistinct amplitude, frequency, and phase.

The set of sinusoidal signals is known as aFourier series.

The frequency spectrum of a signal is the

amplitude and phase components of the signalversus frequency.

Chap 1 - 16

Frequencies of Some Common Signals

Audible sounds 20 Hz - 20 KHz

Baseband TV 0 - 4.5 MHz

FM Radio 88 - 108 MHz

Television (Channels 2-6) 54 - 88 MHz

Television (Channels 7-13) 174 - 216 MHz

Maritime and Govt. Comm. 216 - 450 MHz

Cell phones and other wireless 1710 - 2690 MHz

Satellite TV 3.7 - 4.2 GHz

Wireless Devices 5.0 - 5.5 GHz


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Chap 1 - 17

Fourier Series

Any periodic signal contains spectral components only at discretefrequencies related to the period of the original signal.

A square wave is represented by the following Fourier series:

v(t) =VDC +2VO

sin0t+1

3sin30t+

1

5sin50t+ ...

0=2/T (rad/s) is the fundamental radian frequency and f0=1/T (Hz) isthe fundamental frequency of the signal. 2f0, 3f0, 4f0 , etc. are called thesecond, third, and fourth harmonic frequencies.

Chap 1 - 18

Amplifier Basics

Analog signals are typically manipulated withlinear amplifiers.

Many signal produced by transducers as verysmall in value (weak) and can easily be corruptedby noise.

If a weak signal were to be sampled by an A/Dconverter, much information would be lost.

Amplifiers are designed to provide gain in theform of a scalar value.


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Chap 1 - 19

Amplifier Basics

An idea amplifier would be completely linear,meaning the output would be identical to the inputsignal, except for having a larger magnitude.

Any deviation from this is considered a distortionof the signal, whether intentional or unintentional.

vo(t) = Avi(t)

Amplifiers can also be used to provide current

gain to a signal (power amplifiers).

Chap 1 - 20

Amplifier SymbolAmplifier circuit symbol

First circuit shows an amplifier beingused with a single-ended input

Second circuit shows an amplifier beingused with a differential input

Typically the output of the amplfier issingle ended and reference to acommon ground.

Amplifier voltage gain is:

Current Gain Power Gain

iv

vA o=

ii

iA o= i

ii

AAiv

ivA v==

oo


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Chap 1 - 21

Amplifier Input/Output Response

vi =sin2000tV

Av=-5

Note: negativegain is equivalentto 180 degrees ofphase shift.

Amplifier Power

Since amplifiers are typically used to increase theenergy contained within a signal, the amplifierrequires an external power supply.


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Amplifier Saturation

A typical amplifier powered by power supplies cannotoutput a signal larger than there voltages and in most cases

this limitation is a fraction of a voltage to volts in value. Signal distortion results if an amplifier tries to drive the

output voltage beyond this limit (clipping)

Gain in Decibels

Sometimes it is beneficial or easier to expressgain with a logarithmic measure in dB (decibels)

Due to the wide range of gains contained invarious circuits ( < 1 up to >10,000, gain iscommonly displayed in dB (log)

Voltage gain in decibels: 20log|Av| dB Current gain in decibels: 20log|Av| dB

Power gain in decibels: 10log|Av| dB


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Chap 1 - 25

Amplifier Frequency Response

Low Pass High Pass Band Pass Band Reject All Pass

Amplifiers can be designed to selectively amplify specificranges of frequencies. Such an amplifier is known as afilter. Several filter types are shown below:

Voltage Amplifier


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Four Amplifier Types

Voltage Amplifier Current Amplifier

Transconductance Transresistance

Single Time Constant Networks


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Bode Plots (Low Pass)

Bode Plots (High Pass)


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Chap 1 - 31

Circuit Element Variations

All electronic components have manufacturingtolerances. Resistors can be purchased with 10%, 5%, and

1% tolerance. (IC resistors are often 10%.)

Capacitors can have asymmetrical tolerances such as +20%/-50%.

Power supply voltages typically vary from 1% to 10%.

Device parameters will also vary with temperature andage.

Circuits must be designed to accommodate thesevariations.

We will use worst-case and Monte Carlo (statistical)analysis to examine the effects of component parametervariations.

Chap 1 - 32

Tolerance Modeling

For symmetrical parameter variations

Pnom(1 - ) P Pnom(1 +)

For example, a 10K resistor with5% percenttolerance could take on the following range ofvalues:

10k(1 - 0.05) R 10k(1 + 0.05)9,500 R 10,500


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Chap 1 - 33

Circuit Analysis with Tolerances

Worst-case analysis Parameters are manipulated to produce the worst-case min and

max values of desired quantities.

This can lead to over design since the worst-case combination ofparameters is rare.

It may be less expensive to discard a rare failure than to design for100% yield.

Monte-Carlo analysis Parameters are randomly varied to generate a set of statistics for

desired outputs.

The design can be optimized so that failures due to parameter

variation are less frequent than failures due to other mechanisms. In this way, the design difficulty is better managed than a worst-

case approach.

Chap 1 - 34

Worst Case Analysis Example

Problem: Find the nominal andworst-case values for outputvoltage and source current.

Solution:

Known Information andGiven Data: Circuit topologyand values in figure.

Unknowns: VOnom, VO

min ,VO

max, IInom, II

min, IImax .

Approach: Find nominal valuesand then select R1, R2, and VIvalues to generate extreme casesof the unknowns.

Assumptions: None.

Analysis: Next slides

Nominal voltage solution:

VOnom =VI

nom R1nom

R1nom+R2

nom

=15V18k

18k + 36k= 5V


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Chap 1 - 35

Worst-Case Analysis Example (cont.)

Nominal Source current:

I Inom =

VInom

R1nom+R2

nom =15V

18k+ 36k= 278A

Rewrite VO to help us determine how to find the worst-case values.

VO =VIR1

R1 +R2=

VI

1+R2R1

VO is maximized for max VI, R1 and min R2.

VO is minimized for min VI, R1, and max R2.

VOmax =

15V(1.1)

1+ 36K(0.95)18K(1.05)

=5.87V

VO

min =15V(0.95)

1+ 36K(1.05)18K(0.95)

= 4.20V

Chap 1 - 36

Worst-Case Analysis Example (cont.)

Check of Results: The worst-case values range from 14-17 percentabove and below the nominal values. The sum of the three elementtolerances is 20 percent, so our calculated values appear to bereasonable.

Worst-case source currents:

I Imax =

VImax

R1min +R2

min =15V(1.1)

18k(0.95)+ 36k(0.95)= 322A

IImin =

VImin

R1max +R2

max =15V(0.9)

18k(1.05)+ 36k(1.05)= 238A


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Chap 1 - 37

Monte Carlo Analysis

Parameters are varied randomly and output statistics aregathered.

We use programs like MATLAB, Mathcad, SPICE, or aspreadsheet to complete a statistically significant set ofcalculations.

Chap 1 - 38

Monte Carlo Analysis Result

Histogram of output voltage from 1000 case Monte Carlo simulation.

WC

WC


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Chap 1 - 39

Monte Carlo Analysis Example

Problem: Perform a Monte Carloanalysis and find the mean, standarddeviation, min, and max for VO, IS,and power delivered from thesource.

Solution:

Known Information and GivenData: Circuit topology and valuesin figure.

Unknowns: The mean, standarddeviation, min, and max for VO, IS,and PS.

Approach: Use a spreadsheet toevaluate the circuit equations withrandom parameters.

Assumptions: None.

Analysis: Next slides

Monte Carlo parameter definitions:

VI =15(1+0.2(RAND()0.5))

R1 =18,000(1+0.1(RAND()0.5))R2 = 36,000(1+0.1(RAND()0.5))

Chap 1 - 40

Monte Carlo Analysis Example (cont.)

I I =VI

R1 +R2

Circuit equations based on Monte Carlo parameters:

VO =VIR1

R1 +R2PI =VI I I

Avg Nom. Stdev Max WC-max Min WC-MinVo (V) 4.96 5.00 0.30 5.70 5.87 4.37 4.20II (mA) 0.276 0.278 0.0173 0.310 0.322 0.242 0.238P (mW) 4.12 4.17 0.490 5.04 -- 3.29 --

VS =15(1+ 0.2(RAND() 0.5))

R1 =18,000(1+ 0.1(RAND() 0.5))

R2 = 36,000(1+ 0.1(RAND() 0.5))

Monte Carlo parameter definitions:

Results:


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Chap 1 - 41

Temperature Coefficients

Most circuit parameters are temperature sensitive.

P =Pnom(1+1T+2T2) whereT = T-Tnom

Pnom is defined at Tnom Most versions of SPICE allow for the specification

of TNOM, T, TC1(1), TC2(2).

SPICE temperature model for resistor:

R(T) =R(TNOM)*[1+TC1*(T-TNOM)+TC2*(T-TNOM)2]

Many other components have similar models.

Chap 1 - 42

Numeric Precision

Most circuit parameters vary from less than +/- 1 %to greater than +/- 50%.

As a consequence, more than three significant digitsis meaningless.

Results in the text for the most part will be

represented with three significant digits: 2.03 mA,5.72 V, 0.0436 A, and so on.

01 signals and amplifiers

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