Ee210 digital electronics class lecture 2 september 03 2008
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EE210 Digital Electronics Class Lecture 2 September 03, 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)

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EE210 Digital Electronics Class Lecture 2 September 03, 2008

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Ee210 digital electronics class lecture 2 september 03 2008

EE210Digital ElectronicsClass Lecture 2September 03, 2008


Ee210 digital electronics class lecture 2 september 03 2008

Sedra/SmithMicroelectronic Circuits5/e

Oxford University Press


Ee210 digital electronics class lecture 2 september 03 2008

Introduction to Electronics

3


In this class

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

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


Ee210 digital electronics class lecture 2 september 03 2008

vs (t) = Rsis(t)

Two alternative representations of

a signal source: (a) the Thévenin form, and

(b) the Norton form.


Ee210 digital electronics class lecture 2 september 03 2008

Appendix C

Thévenin’s theorem.


Ee210 digital electronics class lecture 2 september 03 2008

Norton’s Theorem


Th venin norton

Thévenin& Norton

Points to Note:

  • Two Representations are Equivalent

  • Parameters are Related as:

    vs (t) = Rsis(t)

  • Thévenin Preferred When RsLow

  • Norton Preferred When RsHigh


Ee210 digital electronics class lecture 2 september 03 2008

Example C.1

Apply Thévenin’s Theorem to Simplify A BJT Circuit


Ee210 digital electronics class lecture 2 september 03 2008

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

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


Ee210 digital electronics class lecture 2 september 03 2008

Sine-wave voltage signal of amplitude Va and frequency f = 1/T Hz. The angular frequency ω= 2πf rad/s.

Continued 


Ee210 digital electronics class lecture 2 september 03 2008

  • 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 Square-wave Signal in Next Slide.


Ee210 digital electronics class lecture 2 september 03 2008

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


Ee210 digital electronics class lecture 2 september 03 2008

  • 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


Ee210 digital electronics class lecture 2 september 03 2008

FT can be Applied to Non-Periodic Functions of time, such as:

And Provides Frequency Spectrum as a Continuous Function of Frequency, Such As:


Ee210 digital electronics class lecture 2 september 03 2008

The Frequency Spectrum of Previous Arbitrary Non-periodic Waveform


Ee210 digital electronics class lecture 2 september 03 2008

Periodic

Non-Periodic

Periodic Signals Consists of Discrete Freq.

Non-Periodic Signals Contains ALL Freq.

HOWEVER, …


Ee210 digital electronics class lecture 2 september 03 2008

  • 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

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


Ee210 digital electronics class lecture 2 september 03 2008

  • 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


Ee210 digital electronics class lecture 2 september 03 2008

Sampling The Continuous-time Analog Signal in (a)Results in The Discrete-time Signal in(b)


Ee210 digital electronics class lecture 2 september 03 2008

  • 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


Ee210 digital electronics class lecture 2 september 03 2008

  • 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


Ee210 digital electronics class lecture 2 september 03 2008

  • 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

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

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-to-Digital Conversion (Increases Cost as Well)


Ee210 digital electronics class lecture 2 september 03 2008

Block-diagram Representation Of The Analog-to-digital Converter (ADC) – A Building Block of Modern Electronic Systems


Ee210 digital electronics class lecture 2 september 03 2008

  • 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

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


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