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

Two alternative representations of a signal source: (a) the Thévenin form, and (b) the Norton form. v s (t) = R s i s (t)

Thévenin’s theorem. Appendix C

Norton’s Theorem

Thévenin & Norton Points to Note: – Two Representations are Equivalent – Parameters are Related as: v s (t) = R s i s (t) – Thévenin Preferred When R s Low – Norton Preferred When R s High

Apply Thévenin’s Theorem to Simplify A BJT Circuit Example C.1

An arbitrary voltage signal v s (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 V a and frequency f = 1/T Hz. The angular frequency ω = 2 π f rad/s. Continued 

Amplitude V a of Sine-wave Signal Commonly Expressed in RMS = V a / √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 ω o t + 1/3 sin 3 ω o t + 1/5 sin 5 ω o t + …) with ω o = 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 Signals Consists of Discrete Freq. Non-Periodic Signals Contains ALL Freq. HOWEVER, … Periodic Non-Periodic

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 v a (t) – In Frequency-Domain V a (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 = b b b … + b N-1 2 N-1 Where, b 0, b 1,… b N-1 are N bits with value 0 or 1 b 0 is LSB and b N-1 is MSB Binary Number Written as: b N-1 b N-2 … b 0

The Binary Rep (Cont…) Quantizes Analog Sample in 2 N 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

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