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UNIVERSITY OF CALIFORNIA
College of Engineering Electrical Engineering and Computer Sciences Department 145M Microcomputer Interfacing Lab Final Exam Solutions May 21, 1999
1a The transition voltages of an A/D converter are the analog input voltages where the digital output changes between neighboring numbers n and n +1. 1b The Nyquist sampling theorem states that to recover completely an analog waveform from its sampled values, the highest frequency present must be less than one-half the sampling frequency 1c The tri-state buffer is a circuit with digital inputs and outputs, plus a digital select line. The logic state of the select line controls whether the outputs are equal to the inputs or whether the outputs are in a high impedance state. 1d Infinite impulse response digital filter is the special case of the general digital filter yi = A 1 xi − 1 + A 2 xi − 2 +... + AM xi − M + B 1 yi − 1 + ... + BN yi − N where at lest one of the Bi are non-zero. [2 points off for giving the general definition only] [2 points off for stating only that the impulse response is infinite- while this is true it does not demonstrate a understanding of what it is] 1e The comparator circuit has two analog inputs ( V + and V – ) and one digital output ( L ).
If V + > V – then L is high; if V + < V – then L is low. ( L is not defined when V + = V – )
[2 points off for stating that the logic output depends on whether the two inputs are equal or not] 1f The sample and hold circuit has an analog input and an analog output, plus a digital control line. The logic state of the control line controls whether the output is equal to the input or whether the output is held constant.
2a Essential features for the circuit design:
- Pistol switch starts all timers and notifies computer (via input port) to play gunshot sound
- Digital output –> 12-bit D/A converter –> power amplifier –> all 12 speakers
- Each touch plate switch is connected to the corresponding timer stop input and is also connected to a digital input line so that the computer knows when the corresponding swimmer has finished
- All timer outputs are connected via tri-state drivers to form a data bus that is connected to 24-bits of digital input
- Each tristate can be individually selected by the computer using an individual digital output line
- All timers are started by the pistol switch and stopped by the corresponding touch plate switch- this avoids computer delay, which can be unpredictable.
Digital I/O requirements
- 13 bits digital input for pistol and 12 touch plate switches
- 24 bits digital input for timer data values
- 12 bits digital output to D/A for gunshot sound
- 12 bits digital output to select individual tri-state circuits
Plate 1
Pistol
Plate 2
Timer 1
Timer 2
Start Stop Start Stop
24
24
Enable 1
Enable 2
Tr-state drivers
Data bus
12 bit D/A converter
12
Power amplifier
To 12 speakers
16 bit digital input
16 bit digital output
32 bit digital input
16 bit digital output
Micro- computer
2b Hardware and software events 1 Computer loops to detect pistol switch closure 2 Pistol contact closes 3 All12 timer boxes start 4 Computer detects pistol switch closure and sends series of 12-bit words (gunshot sound) to D/A, whose output is amplified and sent to the 12 speakers 5 Computer loops to detect closure of any of the 12 touch plate switches 6 Touch plate n closes and is detected by the computer
1 The low pass filter continuously removes high frequencies from the analog waveform 2 The pulse generator produces a sequence of 10 μs-wide pulses at 65,536 Hz. 3 The leading edge of each 10 μs pulse puts the sample and hold amplifier into hold mode and starts A/D conversion 4 During the 10 μs pulse, the A/D input is held constant during conversion 5 When conversion is complete, the A/D generates a data available pulse 6 The data available pulse is detected by the computer and the data are read 7 The computer repeats step 6 until 2^17 = 131,072 samples are read. 8 The computer multiplies the data by the Hanning window and takes the FFT [ 2 points off if no Hanning window] [3 point off if no FFT] 3d H 0 corresponds to 0 Hz; H 1 corresponds to 0.5 Hz; H65,536 corresponds to 32,768 Hz; H131,071 corresponds to 0.5 Hz 3e A pure harmonic 1000 Hz signal would have equal magnitudes at H 2000 and HM-2000 and smaller side lobes at H2000±1 and HM-2000±1. 3f Because the Hanning window adds side lobes at indices ±1, to appear as separate peaks the two components must be separated by at least three frequency indices, or 1.5 Hz 1.5 Hz
[1.5 to 2.5 Hz was accepted] [2 points off for 1 Hz] [3 points off for 0.5 Hz] 3g The 20,000 Hz harmonic would have equal magnitudes at H40,000 and H M -40,000 = H91, plus side lobes at H40,000±1 and H91,072±1. The 46,536 Hz harmonic would be reduced by a factor of 100 or more by the antialiasing filter before sampling and would appear at H38, and H93,072 (plus side lobes at H38,000±1 and H93,072±1). [1 point off for a smaller amplitude for the higher frequency but the ratio not given] [2 points off if amplitude ratio not mentioned] 3h A 100 Hz fundamental would occur at H 200 and HM- plus side lobes at H200±1 and HM-200±1. 3i The mth harmonic would occur at H m 200 and H M -200 m plus side lobes at H m 200±1 and H M -200 m ±1. [1 point off if H M -200 m not mentioned]
145M Final Exam Grades (18 undergraduate and 6 graduate students): Problem 1 2a 3 Total Average 33.5 52.2 85.5. 171. rms 3.0 8.5 19.5 27. Maximum 36 60 104 200
145M Numerical Grades (18 undergraduates only): Lab total Lab Partic. Midterm #1 Midterm #2 Final Total Average 487.2 93.9 77.0 75.4 170.4 910. rms 11.1 4.7 13.8 13.2 31.4 5 7. 3 Maximum 500 100 100 100 200 1000
145M Letter Grade Distribution Letter Grade Course Totals (1000 max) A+ 966 A 965, 961, 946, 942(G), 941, 941, 937. A– B+ 922, 917, 917, 916, 916(G), 912, 910, 900(G) B 898(G), 896(G), 885, 884(G), 882 B- C+ 824 C C– D+ D 735
(G) = graduate student
