Electronics Design Laboratory Lecture #4. ECEN 2270 Electronics Design Laboratory

Transcription

1 Electronics Design Laboratory Lecture #4 Electronics Design Laboratory 1

2 Part A Experiment 2 Robot DC Motor Measure DC motor characteristics Develop a Spice circuit model for the DC motor and determine model parameters based on experiments alidate the model: compare experimental and simulation results Part B Design a speed sensor circuit (tachometer) that outputs voltage proportional to wheel speed Use LTspice simulations to verify and debug the design Build, test and demo the speed sensor circuit Electronics Design Laboratory 2

3 DC Motor System DC voltages move the motor at some angular frequency. This angular frequency is translated into a frequency by an optical encoder. Inputs: differential voltage DC and motor current I DC 10 < DC < _ I DC Optical Encoder wheel shaft ENCA DC Motor 64:1 gear Outputs: Encoder signals with 50% duty cycle, f enc ω wheel Electronics Design Laboratory 3

4 Experiment 2 Part B: Speed Sensor Circuit Slow Fast Encoder Pulses T enc = 1/f enc = 1/(K e ω) () enc ) Desired Output Min[T enc ]@Max[f enc ] 0@(f enc = 0) (t) Encoder output pulses, frequency f enc [Hz] is proportional to speed It is hard to measure frequency, but easy to measure voltage so we want to translate f enc to a proportional voltage Goal: Convert frequency to voltage Electronics Design Laboratory 4

5 Converting Frequency to oltage Encoder Pulses T enc = 1/f enc = 1/(K e ω) ENC cc 0 t One Shot Output OS cc 0 T ON (Independent of f enc!) t Pulse of width T on generated at each rising edge of the encoder. Same frequency as encoder signal, but different average. OS K CC OS T T ON ENC CC T ON K e Average Output speed cc 0 speed = average < OS > = K OS ω t Electronics Design Laboratory 5

6 Converting Frequency to oltage Encoder Pulses ENC One Shot Output cc 0 T enc = 1/f enc = 1/(K e ω) t OS cc 0 Lower frequency means one shot pulses further apart average value is lower. Average Output speed cc 0 speed = < OS > = K OS ω T ON (Independent of f enc!) OS K CC OS T T ON ENC CC T ON K e t t Electronics Design Laboratory 6

7 Tachometer Block Diagram Optical Encoder One Shot Circuit Average Circuit v speed f enc Ke Electronics Design Laboratory 7

8 Tachometer Circuit One shot Motor with Optical Encoder Average Electronics Design Laboratory 8

9 How to approach the analysis (or design, or debugging) of a complex circuit 1. DON T: dive right in and start writing a lot of loop and node equations You will make an algebraic mess and get nowhere When debugging: don t just build the whole thing and turn it on, expecting it to work first time 2. DO: Break the circuit down into smaller functional blocks that can be separately understood First try to explain in words how each block works Isolate sections that you don t understand. Explain the ones you do understand first. Get the first block to work before moving on to the next Don t try and solve it all at once! Electronics Design Laboratory 9

10 3. DO: For each block, decide what you need to know, and what analysis will be feasible Identify the input and output signals Write simple equations Develop additional constraints based on your understanding of how the circuit is supposed to work Solve the equations for the element values; often there is more than one valid answer Chose impedance levels so that currents and power consumption are reasonable, e.g. ma not A Electronics Design Laboratory 10

11 Tachometer Circuit Blocks Trigger Solved Motor Solved in Part A 555 One shot Low pass filter Electronics Design Laboratory 11

12 555 One Shot: Inside the 555 Timer Comparators SR Latch Output Buffer Comparator Output depends on relative value of both inputs. cc Commonly used to detect signal level 0 SR Latch out Output Q dependent on set input S, and reset input R. Output changes on rising edge of input signal. Logic level 1 corresponds to a voltage of cc. in in in in CC 0 S R Q Q 0 0 Q Q X X t Discharge Transistor Buffer out in Output voltage equals the input voltage. Buffers are used to strengthen signals. The buffer is able to drive large currents. Electronics Design Laboratory 12

13 555 One Shot Inputs: Encoder pulses with 50% duty cycle Outputs: Fixed on time pulse Things we want to know: How does this circuit generate the t on pulse? How long is t on, and how should we choose R 2 and C 2? Electronics Design Laboratory 13

14 555 One Shot Solution ton / R2C2 CC ( 1 e ) 2 3 CC t on R 2 C 2 ln 3 One shot timing t on : must be shorter than shortest T enc Design output pulse t on to set duty cycle at maximum frequency Want t on as long as possible, try to achieve t on = (0.9)MIN[T enc ] Electronics Design Laboratory 14

15 Tachometer Circuit Blocks Trigger Solved Motor Solved in Part A 555 One shot Solved Low pass filter Electronics Design Laboratory 15

16 Equivalent circuit Trigger circuit Inputs: v enc (t), square wave from encoder Outputs: Set pulse going to latch Things we want to know: How is f related to the ground speed of the wheels? (left as exercise for students) How does this circuit generate the set pulse? How long is t trig, and how should we choose R 1 and C 1? t trig The set pulse needs to terminate before it is time to reset the latch. But the datasheet for the 555 timer specifies a minimum pulse width of 1 µsec. Electronics Design Laboratory 16

17 Trigger Circuit Analysis: Preliminaries CC k 15k 3 5 CC Characteristics of silicon p n diode enc enc c1 5 c1 5 D1 acts as a switch, creating two equivalent circuits depending on A B ENC + c1 = TRIG = ( ) Equivalent circuit B is solved visually. All nodes have known voltages! Equivalent circuit A is unknown. Inputs: enc Outputs: TRIG Electronics Design Laboratory 17

18 Trigger Circuit: Waveforms t trig B A B D 1 does not allow TRIG > CC so v C1 = 0 Electronics Design Laboratory 18

19 Assume t = 0 at the falling edge of enc Redraw the equivalent circuit in the time domain Trigger Circuit: Solution Using the Laplace transform Or with the Laplace transform Then solve for capacitor voltage c1 t trig is the time at which c1 = + Now use partial fraction expansion to take inverse Laplace transform; the result is: v The trigger circuit comparator causes the set pulse to end when v C1 = CC /3, at time t = t trig. Hence: v Solving for t trig CC (1 C1( t) CC 1 t e 3 ) 3 trig / R1C 1 CC e t trig CC C1( ttrig ) CC 1 t trig / R C 1 e 1 t trig / R C 1 R C ln 2 1 Electronics Design Laboratory 19

20 Tachometer Circuit Blocks Trigger Solved Solved Motor Solved in Part A 555 One shot Solved Low pass filter Electronics Design Laboratory 20

21 Low Pass Filter Circuit Input: Pulse width modulated signal OUT Output: speed signal having a DC value proportional to f Things we want to know: How does this circuit operate on the pulse width modulated OUT signal to produce the speed signal? How should we choose R 3 and C 3? Electronics Design Laboratory 21

22 Low Pass Filter Circuit: Analysis The pulse width modulated signal OUT(t) can be represented by Fourier analysis as a DC component 0 plus a sum of sinusoids called harmonics: The amplitude spectrum is a plot of the harmonic amplitudes vs. frequency: The harmonics have frequencies that are integral multiples of the fundamental frequency f. The DC component is given by the average value: We want to attenuate the harmonics (frequencies above DC) and leave the DC component untouched. Electronics Design Laboratory 22

23 Filter design The effect of the R 3 C 3 filter on each individual harmonic can be found by phasor analysis of the circuit: use phasors to solve the circuit and find how the amplitude of a sinusoid is changed by the circuit, as a function of frequency. We want to choose R 3 and C 3 so that the filter passes the DC component and any very low frequency variations that occur as a result of the changing speed of the robot. But we want the filter to reject the components of OUT at the fundamental frequency f and its harmonics. So the filter should have a transfer function (i.e., the ratio of its output voltage amplitude to its input voltage amplitude, vs. frequency) that looks like this: Use phasor analysis to solve for the transfer function of the R 3 C 3 filter. Select appropriate values for R 3 and C 3., Electronics Design Laboratory 23

24 R1, C1 Summary of Time Constants in the Tachometer circuit R 1 & C 1 1s < t trig << t on C 1 >> capacitance at node TRIG R 2 & C 2 R 1 >> R encoder R2, C2 Set t on to determine output voltage of speed sensor at maximum speed (based on CC and duty cycle) R3, C3 R 3 & C 3 Low pass filter PWM output; determines voltage ripple on the speed sensor output voltage R3*C3 >> lowest expected PWM period R3*C3 < desired response time of the speed sensor (e.g. << 1 sec) Electronics Design Laboratory 24