ELEC242 Assignment 2

ELEC242 Assignment 2 2019
Quadrature Encoders
Due Friday, November 1st, 11:59pm (Week 12).
The image below shows the disk for a quadrature encoder. This device creates a series of pulse
strings when a shaft rotates, and is used to measure angle or speed of a shaft.
There are two rings of alternating back and white areas. The inner
ring is the ‘A’ ring, and the outer ring is the ‘B’ ring. Each ring has a
sensor that returns a ‘1’ when faced with white, and a ‘0’ when faced
with back. These sensors output two pulse trains, normally called ‘A’
and ‘B’ as per the ring. They are offset, and depending on whether the
shaft is turning clockwise or anti-clockwise the A channel rising edge
will lead or trail the B channel rising edge.
You are to design a circuit, and produce the Sum of Products (SoP)
terms for that circuit, to create a counter that allows us to determine where the shaft is currently
There are several parts to this assignment. For a Pass mark your counter must give an accurate
position count, incrementing or decrementing as the shaft is rotated. For a Credit or Distinction
mark you need to add in timing information for your circuit and calculate what is the maximum
speed at which the shaft can rotate for your circuit. For a High Distinction mark you circuit must
capture very high precision information about the shaft’s rotation, and must be completely self
clocking, along with the associated timing information.
It is expected that an average student will spend 5 hours to achieve a pass mark on this assignment.
Your submission MUST be fully typeset. No handwritten/scanned work will be accepted.
Submission must be made through Turnitin. Turnitin will require the text of the submission to be
machine scanable.
All SoP equations must be clear and easily legible.
Part 1:
You have a quadrature encoder connected to a shaft. The waveforms for that encoder are shown
below for both clockwise and counter-clockwise rotation. The design states that clockwise rotation
will cause the “position” to increase, and counter clockwise rotation will cause the “position” to
The encoder produces 18 pulses per revolution from each of the A and B channels. Each pulse
would be a 50% duty cycle is the encoder is rotating at a constant angular velocity. The pulses vary
in duration depending on the encoder’s velocity.
Clockwise rotation of the encoder:
Counter-clockwise rotation of the encoder:
The inputs to your circuit are A, B and RESET. The outputs are POSN0 to POSN7, a signed twos
complement number with POSN0 the least significant bit, and POSN7 the most significant bit.
These outputs are always enabled.
Using the A signal as the clock for your circuit. use the B signal and the current position count to
determine the new position count.
Design a circuit using the three specified inputs; A, B and RESET. The A input should be used as
your clock signal. You need to create any Karnaugh maps required, and eventually write out SoP
equations. Show your working for the SoP equations for the position counter. The equations do not
have to be minimal is the non-optimality increases readability.
You can create either an up/down counter directly, or you can have a register interconnected with a
full adder. One of these is a better solution.
You are limited to a maximum of 8 inputs on a D flip flop.
Part 2:
Assuming the following timings:
A D flip flop clock rising edge to Q output valid, minimum 40ns
A D flip flop D input valid BEFORE clock rising edge, minimum 10ns
A NAND gate, or inverter, any number of inputs, change of input to output, minimum 10ns
Calculate the minimum time required to process the quadrature signals, and hence the minimum
time between clock pulses.
Calculate the maximum RPM that the encoder can turn so that the pulses do not breech the
minimum time requirements.
Part 3: (This part is hard)
The above parts only increment or decrement the position count on the rising edge of the A signal.
We can do better than this. Review how a D flip flop works internally. We want to use both the
rising and the falling edge of both the A and the B signals to clock our circuit. This will give us four
times the resolution for the counter, boosting it to 72 positions per revolution.
Also, because we have more pulses per revolution we want to increase our position count to 16 bits.
Finally, minimise the time taken for the counter through the use of look ahead techniques we have
talked about in class.
Design a circuit that updates the position count on either the rising or falling edge of both A and B
Draw a schematic diagram of the circuit, and create the SoP equations for the circuit.
Calculate the timings and show the critical path.
What is the maximum speed (in RPM) that the encoder can turn so that the pulses do not breech the
minimum time requirements.

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