1. EE210 Digital Electronics Class Lecture 2 September 03, 2008

2. Sedra/Smith Microelectronic Circuits 5/e
2/27/2019
Sedra/Smith Microelectronic Circuits 5/e
Oxford University Press

3. Introduction to Electronics
2/27/2019
Introduction to Electronics 3

4. 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

5. 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

6. vs (t) = Rs is(t) Two alternative representations of
a signal source: (a) the Thévenin form, and
(b) the Norton form.

7. 2/27/2019
Appendix C
Thévenin’s theorem.
sedr42021_C01a.jpg

8. 2/27/2019
Norton’s Theorem
sedr42021_C02a.jpg

9. 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

10. Example C.1 Apply Thévenin’s Theorem to Simplify A BJT Circuit
2/27/2019
Example C.1
Apply Thévenin’s Theorem to Simplify A BJT Circuit
sedr42021_C03a.jpg

11. 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

12. 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

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

14. 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.

15. v(t) = 4V/π (sin ωot + 1/3 sin 3 ωot + 1/5 sin 5 ωot + …)
2/27/2019
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

16. 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

17. FT can be Applied to Non-Periodic Functions of time, such as:
And Provides Frequency Spectrum as a Continuous Function of Frequency, Such As:

18. The Frequency Spectrum of Previous Arbitrary Non-periodic Waveform

19. Periodic
Non-Periodic
Periodic Signals Consists of Discrete Freq.
Non-Periodic Signals Contains ALL Freq.
HOWEVER, …

20. 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)

21. 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

22. 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

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

24. 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

25. 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

26. 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

27. 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 = b b b … + 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

28. 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)

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

30. 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

31. 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