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EE210 Digital Electronics Class Lecture 2 September 03, 2008

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EE210Digital ElectronicsClass Lecture 2September 03, 2008

Sedra/SmithMicroelectronic Circuits5/e

Oxford University Press

Introduction to Electronics

3

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

- 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) = Rsis(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

Points to Note:

- Two Representations are Equivalent
- Parameters are Related as:
vs (t) = Rsis(t)

- Thévenin Preferred When RsLow
- Norton Preferred When RsHigh

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

- 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 Square-wave 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)

- 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

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

- 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)

Block-diagram Representation Of The Analog-to-digital 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

We Will Continue to Discuss:

Chapter 1: Introduction to Electronics

Topics:

1.4 Amplifiers

1.7 Logic Inverters

1.8 Circuit Simulation Using SPICE