Assignment, Week 1: Read Bobrow, Ch. 10: Sec. 10.5; Ch. 3 (RC charging and discharging, response of circuits to pulses, particularly secs. 3.3 and 3.4, integrator, differentiator); Ch. 7: 7.3 (BJT cutoff and saturation; emitter-coupled Schmitt trigger; switching time – here are Notes on SPICE analysis of a BJT Schmitt trigger), 544-546 (MOSFET as switch).
- For Lab, the Schmitt Trigger lab writeup has the following problem to work in your lab notebook: prove the equation for Vth in terms of Vbb and Vout. Hint: use the Thevenin equiv. of the voltage divider formed by Vbb , R1 and R2.
- Problems (due Wednesday, 1/12/11): 10.70, 10.71, 10.75(b,c), 10.77(a), 3.33.
- Notes: For 10.75, refer to Table 7.3 on p. 491 of Bobrow for the assumed values of VBE and VCE when an npn BJT is in saturation (ON) and for the maximum value of VBE to remain in the cutoff state. "The low voltage" refers to v0 when Q1 is OFF and Q2 is ON.
For 3.33, find the Thevinen equivalent of the voltage source and 3 resistors driving the capacitor. Also, assume the voltages and currents have reached their steady-state values prior to t=0.
- Problems (due Wednesday, 1/12/11): 10.70, 10.71, 10.75(b,c), 10.77(a), 3.33.
Assignment, Week 2: Read Lab 11 writeup before coming to class Monday. Read Bobrow, Ch. 5: 5.5-5.7 (Laplace transform circuit analysis). Notice that the Laplace transformation solutions are complete solutions to the circuit differential equations, including the effect of the initial conditions (zero or nonzero). Figures 5.38(c) and 5.39(c) show how to include nonzero initial conditions for inductors and capacitors, respectively.
- Problems (due Friday, 1/21/11): 3.9(e) (assume zero initial conditions), 5.59(c), 5.61(b), 5.68 (assume zero initial conditions), 5.76 (assume zero initial conditions).
- For the problems in Ch. 5, refer to the table of Laplace transforms linked in Week 2 of the class outline above (or here). In particular, note the Laplace transformation frequency domain relations for circuit elements (assuming zero initial conditions):
- ZR(s) = R
- ZL(s) = sL
- ZC(s) = 1/(sC).
- These are the same relations we worked with last quarter when dealing with phasors with complex frequency s. This is discussed in the text in Sec. 5.7. Some of the problems also require use of the method of partial fractions, discussed in Sec. 5.6.
- We assume you have some familiarity with Laplace transforms from Math 22B. We will go over examples in class Wednesday.
- For the problems in Ch. 5, refer to the table of Laplace transforms linked in Week 2 of the class outline above (or here). In particular, note the Laplace transformation frequency domain relations for circuit elements (assuming zero initial conditions):
- Optional further reading: you may be interested in the section, "Introduction to Communications," Sec. 10.6.
Assignment, Week 3: Read material in Bobrow on binary numbers, Boolean algebra and combinational logic circuits, namely Ch. 11 and Sec's 1 and 2 of Ch. 12 plus these notes on logic gates and Boolean algebra.
- Problems due Wed. 1/26/11: Use Laplace transform techniques to solve the following problems from Ch. 5: 5.77, 5.83 (find v(t) only), 5.86 (find i(t) only). Also
- Special Problem 1:
- Find the output v2(t) for the high pass RC filter shown in Fig. 5.5 of Bobrow for a ramp input v1(t) = α t u(t), where α is a constant.
Assume v1=v2=0 for t<0. Recall that ωC = 1/RC. - Evaluate v2(t) for ωC = 10 000 rad/s and α = 10 V/s; sketch the output waveform.
- Why might you expect the output to be approx. constant if v2 << v1? Find the output voltage for t >> RC (steady state output).
- Find the rise time of v2 (time required to go from 10% to 90% of the steady state voltage).
- Find the output v2(t) for the high pass RC filter shown in Fig. 5.5 of Bobrow for a ramp input v1(t) = α t u(t), where α is a constant.
- Special Problem 1:
Assignment 4:
- Read 7.4-7.6, 8.4 to get an overview of logic circuit families such as TTL, Schottky TTL, ECL and CMOS. We will discuss simplified models in class (notes here or in Week 4 of the Class Outline, above); 12.3 (flip-flops and sequential circuit introduction – the first part of this section is needed for Lab 13.).
- Problems (due Wednesday, 2/2/11): Bobrow, 11.22, 11.24, 11.27, 11.34, 11.37, 11.45, 11.51(b): make a Karnaugh map, use it to express the function in simplified sum-of-products form and implement with two- and three-input NANDs and inverters; 11.53(c), 11.57(b): also implement with two- and three-input NANDs and inverters.
Assignment 5:
- Read Bobrow, Sections 13.1 - 13.3 and the notes on Sequential Circuit Design from Week 6 of the course outline (above).
- Further reading: Bobrow, 13.4 (the section on DACs and ADCs is needed for the ADC lab next week).
- The text by Horowitz and Hill (H&H) has more detailed information and valuable lore about the material we are covering and includes an introduction to some needed additional topics such as programmable logic devices (PLDs). A guide to relevant material is as follows:
- H&H Sec. 8.15-8.29, 8.33-8.35: logic and sequential circuit design including basic PLD applications; logic circuit pathologies.
- H&H Ch. 9 through Sec. 9.14: logic families, interconnections, do's and don'ts.
- H&H Sec. 9.15-9.25: ADC's and DAC's. Fig. 9.47 shows a basic DAC similar to the one used in Exp't 15.
- H&H will be the primary text when we talk about microcomputers.
- Problems (due Friday, 2/11/11): Bobrow, 12.16(b), 12.19, 12.34, 12.37(also make a state diagram), 13.12(a). (One or two more may be added.)
Assignment 6:
- Reading: continue with the extensive reading material in Assignment 5.
- Problems (due Wednesday, 2/16/11): this set of 4 problems.
- Note on Assignment 6:
- (a) Maximum Clock Frequency: the maximum clock frequency (inverse of minimum clock period) for a synchronous sequential circuit was discussed in class. The minimum clock period is the sum of
- the flip-flop delay (assuming all ff's are the same)
- plus the sum of the gate delays in the longest path from a flip-flop output to a flip-flop input (with external inputs to the circuit itself held constant)
- plus the flip-flop setup time.
- Use worst case values.
- (b) Setup and Hold times: the flip-flop inputs of a synchronous sequential circuit must be held constant during the flip-flop set-up and hold times. Failure to do this can lead to an unexpected transition or to a metastable state (see Horowitz and Hill, pp. 510-511, 552.)
- (c) Asynchronous inputs: an asynchronous external input signal is one which can occur at a random time not synchronized with the system clock. It could change state during the times the inputs are supposed to be steady. An asynchronous signal can be synchronized with the system clock by putting it through one or two stages of D flip-flops with clock inputs connected to the system clock before connecting it to the circuit. This way the sequence of the main counter is protected from malfunction due to the asynchronous nature of the external signal.
- (d) Glitches: a glitch is an undesired short signal arising in an electronic circuit. A glitch can occur if logic (such as an AND) can produce a valid output momentarily as inputs change from one state to another even if the state detected is not the initial or final state. For example, consider F=BA, the AND of A and B corresponding to a two bit binary number from a binary counter circuit (A being the less significant bit). F would be 1 in the state B=1, A=1 ("3") and could be used to detect ("decode") this state. BA could also be 1 for a short time as the counter made the transition from "1" (01) to "2" (10) if A stayed high for a brief time after B changed to 1. If you were trying to detect state "3" to reset the counter (to count modulo 3, for example), it could be reset prematurely by the glitch. Since the glitch is short, it might cause the reset only intermittently. Also, since the pulse is short, it may be hard to see on an oscilloscope. Not all transitions generate glitches. For example, in going from "0" to "1," only one input changes, so there would be no glitch on F for that transition. See figure:
- (a) Maximum Clock Frequency: the maximum clock frequency (inverse of minimum clock period) for a synchronous sequential circuit was discussed in class. The minimum clock period is the sum of
Assignment 7:
- Problems due Friday, March 4, 2011: This set of 6 problems.
- Continue reading the material in Horowitz and Hill from Assignment 5 on programable logical devices (PLDs). In Chapter 8, there are examples of implementing a simple combinational circuit and a finite state machine with a PLD using a hardware description language called CUPL. Wikipedia has a good overview and an introduction to hardware description languages such as VHDL. Many specialized digital applications are implemented with complex PLDs known as FPGAs. One common use in experimental particle physics is for testing individual modules used for tracking particles. If you would like to learn more about using PLDs, a good place to start is Digital Design: Principles and Practices by Wakerly.
- Microcomputers, microprocessors and microcontrollers
- In the remainder of this course, we will emphasize Atmel AVR microcontrollers and the Arduino prototyping platform. Many of the microcontroller concepts are similar to those described for the Motorola 68000 processor in Horowitz and Hill. But the Atmel microcontroller is an "all in one" device with AVR processor, EEPROM, SRAM and Flash RAM, timer/counters, analog and digital I/O pins and a built-in ADC in advanced models.
- We will begin with the Arduino, based on the Atmel Mega168 microcontroller, to get a feeling of what the system can do from a high-level perspective. This will be the subject of Lab 17.
- Then we will look at the AVR microcontroller structure using as an example the simpler AT90S85815. In Lab 18, we will experiment with AVR assembly language using the AVR Studio development system. Also, we will examine a more advanced Arduino application developed by UC Davis Physics alumnus Dr. Mike Madison. This digitizes and plays back signals at a 62.5 kHz sampling frequency.
- Specific general topics:
- Binary Arithmetic, Hexadecimal Notation, 2's Complement Negative Numbers Review - Bobrow, Secs. 11.1, 11.2 and Horowitz and Hill, Sec. 10.23; ASCII Code - Horowitz and Hill, Sec. 10.19 (pp. 720-722).
- Programming and operating system concepts: Horowitz and Hill, Secs. 10.17-10.18.
- Microprocessor overview with Motorola 68000 processor and instruction set: Horowitz and Hill, Ch. 11, pp. 743-752 (once over lightly).
- The M68000 processor architecture and instruction set provide a good basis for an introduction to microcomputer concepts. It was used for early graphical user interface (GUI) computer systems from Sun, Apple, HP, Commodore Amiga and Atari as well as for data acquisition and process control applications (e.g., VME bus systems). It has been used in game systems (e.g., Atari "Marble Madness" arcade game, Sega Genesis), Palm PDAs and TI calculators as well. It is an example of a complex instruction set computer (CISC) as opposed to a reduced instruction set computer (RISC) such as the Atmel AVR.
- Read the material on Arduino programming as indicated in the Lab 17 writeup. Here are the appropriate web links:
- ATMega168 microcontroller overview
- Arduino Wikipedia overview
- Arduino home page
- Getting Started
- Introduction
- Windows installation and use
- Development environment
- Tutorial home page
- Foundations page
- For the vital details on how the instructions and functions work, refer to the reference and extended reference sections. The extended reference page includes functions to use external interrupts.
- See the libraries section for information on valuable extended capabilities such as Ethernet communication (using add-on hardware), LCD display drivers and servo motor control.
- The extended reference page also contains the following key information:
"The Arduino language is based on C/C++ and supports all standard C constructs and some C++ features. It links against AVR Libc and allows the use of any of its functions; see its user manual for details."- This provides a window into developing AVR code directly in C for more substantial projects. The system has some C++ features plus the ability to include assembly language operations in-line or in separate routines. .
Assignment 8:
- Problems: AVR Review Exercises for Assignment 8 on SmartSite (not to be turned in). The solutions are there too.
- Reading:
- Atmel AVR processor overview. Although the last two labs use the Arduino system with its Atmel Mega168 microcontroller, we will study the AVR architecture and instruction set with a simpler version, the AT90S8515.
- Apparently a good overview of Atmel AVR and its development history from Wikipedia
- Download the manual for the AT90S8515 microcontroller
- Also get the Novice's Guide to AVR Development
- And the Atmel AVR Instruction Set Manual
- You are encouraged to register and get the AVR Studio program to allow you to write assembly language programs and run them with a simulator.
- Here is a Beginner's Introduction to the Assembly Language of Atmel AVR Microprocessors which explains assembly language constructs and programming (translated from German).
- Here is the website containing the linked file above. It has a number of good examples of simple AVR applications using assembly.
- For example, this program demonstrates use of the RS232 serial input/output port and manipulation of ASCII characters. It also shows loops and subroutines in action to access a buffer in SRAM.
- Atmel AVR processor overview. Although the last two labs use the Arduino system with its Atmel Mega168 microcontroller, we will study the AVR architecture and instruction set with a simpler version, the AT90S8515.
- As stated above, we will experiment with AVR assembly language using the AVR Studio development system in Lab 18.
- In class, we will discuss sampled waveforms, the sampling theorem, the Nyquist critical frequency and aliasing. Also, we will examine a more advanced Arduino application developed by UC Davis Physics alumnus Dr. Mike Madison. This digitizes and plays back signals at a 62.5 kHz sampling frequency. It uses assembly code to address Mega168 microcontroller registers and an interupt service routine in an Arduino program. Slides will be posted in SmartSite. The sampling theorem and aliasing (to be covered in 116C), interrupts and the Madison Arduino application will not be on the final exam.