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EE210 Digital Electronics
Class Lecture 2
March 20, 2008
Sedra/Smith
Microelectronic
Circuits 5/e
Oxford University Press
Introduction to Electronics
3
In This Class
We Will Discuss Following Topics :
1.1 Signals
Thévenin & Norton Theorem
(Append. C)
1.2 Frequency Spectrum of Signals
1.3 Analog and Digital Signals
1.1 Signals
• Signals Contain Information
• To Extract Information Signals Need to be
PROCESSED in Some Predetermined
Manner
• Electronic System Process Signals
Conveniently
• Signal Must be an Electric Entity, V or I
• Transducers Convert Physical Signal into
Electric Signal
vs (t) = Rs is(t)
Two alternative representations of
a signal source: (a) the Thévenin form, and
(b) the Norton form.
Appendix C
Thévenin’s theorem.
Norton’s Theorem
Thévenin & Norton
Points to Note:
– Two Representations are Equivalent
– Parameters are Related as:
vs (t) = Rs is(t)
– Thévenin Preferred When Rs Low
– Norton Preferred When Rs High
Example C.1
Apply Thévenin’s Theorem to Simplify A BJT Circuit
An arbitrary voltage signal vs(t).
Signal is a Quantity That Varies in Time.
Information is Contained in the Change in
Magnitude as Time Progresses.
Difficult to Characterize Mathematically
1.2 Frequency Spectrum of Signals
• Signal (or Any Arb. Function of Time)
Characterization in Terms of Frequency
Spectrum, using Fourier Series/Transform
• FS and FT Help Represent Signal as Sum of
Sine-wave Signals of Different Frequencies
and Amplitudes
• Use FS When Signal is Periodic in Time
• Use FT When Signal is Arbitrary in Time
Sine-wave voltage signal of amplitude Va
and frequency f = 1/T Hz. The angular
frequency ω = 2πf rad/s.
Continued 
• Amplitude Va of Sine-wave Signal
Commonly Expressed in RMS = Va / √2
• Household 220 V is an RMS Value
• FS allows us to Express ANY Periodic
Function of Time as Sum of Infinite
Number of Sinusoids Whose Frequencies
are Harmonically Related, e.g., The Squarewave Signal in Next Slide.
Using FS Square-wave Signal can be Expressed as:
v(t) = 4V/π (sin ωot + 1/3 sin 3 ωot + 1/5 sin 5 ωot + …)
with ωo = 2 π/ T is Fundamental Frequency
Sinusoidal Components Makeup Frequency Spectrum
• The Frequency Spectrum (Also Known As The Line
Spectrum) Of The Previous Periodic Square Wave
• Note That Amplitude of Harmonics Progressively
Decrease
• Infinite Series Can be Truncated for Approximation
FT can be Applied to Non-Periodic
Functions of time, such as:
And Provides Frequency Spectrum as
a Continuous Function of Frequency,
Such As:
The Frequency Spectrum of Previous
Arbitrary Non-periodic Waveform
Periodic
Non-Periodic
Periodic Signals Consists of Discrete Freq.
Non-Periodic Signals Contains ALL Freq.
HOWEVER, …
• The Useful Parts of the Spectra of
Practical Signals are Confined to
Short Segments of Frequency, e.g.,
Audio Band is 20 Hz to 20kHz
• In Summary, We can Represent A
Signal :
– In Time-Domain va(t)
– In Frequency-Domain Va(ω)
1.3 Analog and Digital Signals
• This is an Analog Signal as it is Analogous
to Physical Signal it Represents
• Its Amplitude Continuously Varies Over Its
Range of Activity
• Digital Signal is Representation of the
Analog Signal in Sequence of Numbers
• Each Number Representing The Signal
Magnitude at An Instant of Time
• Let us Take the Analog Signal and Convert
it To Digital Signal by SAMPLING
• Sampling is a Process of Measuring The
Magnitude of a Signal at an Instant of
Time
Sampling The Continuous-time Analog Signal in (a)
Results in The Discrete-time Signal in (b)
• Original Signal is Now Only Defined at Sampling
Instants – No More Continuous, Rather Discrete
Time Signal, Still Analog as Mag. Is Cont.
• If Magnitude of Each Sample is Represented by
Finite Number of Digits Then Signal Amplitude
will Also be Quantized, Discretized or Digitized
• Then, Signal is Digital --- A Sequence of Numbers
That Represent Mag. of Successive Signal Samples
• The Choice of Number System to Represent
Signal Samples Affects the Type of Digital
Signal Produced and Also Affects the
Complexity of Dig. Circuits
• The BINARY Number System Results in
Simplest Possible Signals and Circuits
• In a Binary Number Digit is Either 0 or 1
• Correspondingly, Two Voltage Levels (Low
or High) for Digital Signal
• Most Digital Circuits Have 0 V or 5V
• Time Variation of a Binary Digital Signal
• Note That: Waveform is a Pulse Train with 0 V
Representing 0 or Logic 0 and 5V Rep. Logic 1
Binary Rep. of Analog Signal
To use N Binary Digits (bits) to Represent
Each Sample of The Analog Signal, the
Digitized Sample Value Can be as:
D = b0 20 + b1 21 + b2 22 + … + bN-1 2N-1
Where,
b0 , b1 ,… bN-1 are N bits with value 0 or 1
b0 is LSB and bN-1 is MSB
Binary Number Written as: bN-1 bN-2 … b0
The Binary Rep (Cont…)
• Quantizes Analog Sample in 2N Levels
• Greater the Number of Bits (Larger N)
Closer the Digital Word D Approx. to the
Magnitude of the Analog Sample
• Large N Reduces the Quantization Error
and Increases the Resolution of Analog-toDigital Conversion (Increases Cost as Well)
Block-diagram Representation Of The Analog-todigital Converter (ADC) – A Building Block of
Modern Electronic Systems
• Once Signal is in Digital Form it Can be
Processed by Digital Circuits
• Digital Circuits also Process Signals which
do Not Have Analog Origin, e.g., Signals
Representing Digital Computer Instruction
• As Digital Circuits Deal With Binary
Signals Their Design is Simpler Than of
Analog Circuits
• While Digital Circuit Design has Its Own
Challenges, It Provides Reliable and
Economic Implementations of Many Signal
Processing Functions not Possible With
Analog Circuits
In Next Class
We Will Continue to Discuss:
Chapter 1: Introduction to Electronics
Topics:
1.4 Amplifiers
1.7 Logic Inverters
1.8 Circuit Simulation Using SPICE