Circuits with Feedback: Clock, Counter, and Mux, Names
Objectives
We investigate circuits with feedback. Depending on the number of signal inversions, we will obtain a free running oscillator and an octave generator.
Create a ring oscillator using a closed loop with 3 inverters (7404). Note that two crucial points about a ring oscillator are: (1) there must be an odd number of signal inversions around the loop, and (2) any transition travels twice around the loop to bring the circuit back into the starting state.
i. Use LogicWorks to simulate the timing of the circuit.
ii. Develop a general formula for the frequency of oscillation of the circuit as a function of the propagation delay of the gates in the circuit. Now use this formula with the delay times found in the TTL Data Book for the 74LS04 to calculate an expected period of oscillation. Give the name for all delay values used (e.g. "tplh").
iii. Build the ring oscillator, measure the period of the wave of the ring oscillator, and compare it with the expected period.
iv. Change the number of inverters to 5 and repeat the measurement.
v. Attempt to explain any differences that you find, taking into account that the values given in the TTL data book are average and worst case times.
Study the 555 timer chip. Connect pin 1 to ground, pin 8 to 5V, pin 2 to pin 6, pin 3 to output pin 4 to 5V. Put between ground and pin 4, pin 5, pin 6 capacitors of 0.1uF, 0.01uf, C1, respectively. Connect between pin 6 and pin 7 with resistor Rb, pin 7 and pin 8 with resistor Ra. From the formulas given for the period and pulse length, compute the values of resistance and capacitance required to obtain a square wave of 500 us period and 75% duty cycle. (Note that C is in farads, and R is in ohms).
Period = 0.7 (Ra + 2 Rb) Cl
Pulse length = 0.7 (Ra + Rb) Cl
Do not plan to use a resistor of less than 1Kohms. In building this circuit, use resistors of 1000 ohms or bigger and whatever capacitors you have in your parts packet. The 555 timer can draw large amounts of current for short periods of time when the output changes state. For this reason, it is important to put a 0.1uF bypass capacitor from the 5V pin, pin 8 to ground. This capacitor will minimize spikes that can upset the rest of your circuit. In general it is good practice to put bypass capacitors liberally throughout your design on the power pins of ICs.
i. What is the expected Period and duty cycle for your generator?
ii. What is the observed period and duty cycle?
iii. If the period that you observe is not what you calculated, suggest some reason why.
In music, the "A" one octave above middle "A" is at twice the frequency of middle "A" or 880 Hz. Mechanical oscillators, like strings in a piano, do not tend to stay perfectly in tune with each other, but by using divideby2 counters to generate octaves, the frequency ratio will always be exact with a digital tone generator. Design an octave generator, using the 555 timer as a clock input to a counter, and using the 74153 4:1 multiplexer to select one of 4 octaves, from the counter outputs. The 4 counter outputs go to the 4 multiplexer inputs. Use two debounced switches to select among octaves on the multiplexer. The multiplexer output is fed into at 7405/7406 inverter to drive the speaker.
i. Draw your design in LogicWorks. You may use the clock symbol in place of the 555 circuit..
ii. Build the octave generator circuit.
iii. Connect one side of a speaker to 5V and the other side to the output of an 7405/06 open collector inverter through a 330 ohm resistor to protect the inverter from burnout.
iv. Demonstrate to a tutor that you can select each of 4 octave tones with your two switches. _______________________________(signed by a tutor)
1. Include a hardcopy of the logic diagram and timing of 1.i. Describe the formula in 1.ii, the comparison in 1.iii, 1.iv. Explain the differences we find in 1.v.
2. Describe the derivation in 2.i. Report the result in 2.ii. Explain the result in 2.iii.
3. Include the logic diagram of 3.i. Include this page with the signature of a tutor on 3.iv.
4. A brief description of the contribution of each team member.