Download Digital-to-Analog Conversion PWM PWM

Phys 253 - Lecture 4:
• D/A Conversion, PWM
Week 4 Lab:
• Lab 4 – Motor Control
• Wall-climbing Demo (Bernhard)
Digital-to-Analog Conversion
PWM
• Motors - Intro ((Jon))
• Mech Design 2 (Robin Coope – separate notes)
1
D/A Conversion and power circuits
2
D/A conversion: Resistor ladders #1
(binary weighted DAC)
When would you like to produce an output signal that is more
than just on or off? (e.g. brightness of light, speed of a motor,
current through electric heater, etc…. )  Analog Outputs
An op-amp summing circuit
Vout = - (50k / R) * 1.0V
Digital-to-Analog Conversion (DAC):
10110011, 01010101, …
V
For a 4 bit ladder, what is the
maximum |Vout| ?
t
1) 4.375 V
Two simple schemes we will use in 253 (of many possible schemes)
2) 5V
1. Resistor ladders (combine multiple digital outputs into one analog output)
2. Pulse Width Modulation (turn one digital output on and off at high
frequency)
3) 9.375 V
4) 10V
3
D/A conversion: Resistor ladders #2
4
D/A conversion: Pulse Width Modulation
(PWM)
(R-2R Ladder)
• This scheme uses a digital output to produce an analog voltage by
digitally controlling the % of time that the output is high.
• The TIME AVERAGED voltage produced can therefore be almost
continuously variable.
Tpulse
Duty cycle = Tpulse/Tpwm
5V
Another configuration for an op-amp summing circuit. What
are the advantages/disadvantages of this arrangement?
0
t
Tpwm
5
6
1
D/A conversion: PWM
PWM
Duty
Cycle
D/A conversion: PWM
PWM
Duty
Cycle
Average voltage:
0V
0
0
0
25%
t
50%
0.25 * 5 V = 1.25 V
5V
2.5 V
5V
t
0%
Average voltage:
4.75 V
5V
0
t
t
95%
7
8
D/A conversion: PWM
PWM
Duty
Cycle
Average voltage:
Next:
2.5 V
High-Current Circuits
and Motor Control
50%
0
t
• Must be low-pass filtered to be used as an analog output
• To avoid ripple, low-pass filter at f << fpwm. Note that this can
place a severe limit on the output bandwidth.
• Resolution is limited by minimum switching time of the
digital output.
9
High current and inductive loads
Example load - High current and inductive loads
Digital Outputs do not provide sufficient current to drive anything other
than output signals to other electronics.
Digital outputs can be “amplified” to turn on devices that require high
currents. Mechanical/solid-state relays or Transistors can be used as
electrically-controlled switches…
Electromechanical relay
V1
5V
+V
BJT used as a
switch for load
L1 (image from
Lecture 1)
S1
+ V2
5V
• LM311 sinks up to
50mA (works but poor
choice)
L1
Dout
5V
+V
U1
LM311
R1
1k
RLY1
Q1
2N3904
Q1
3904
R2
100k
R3
100k
11
R2
100
5V
+V
• Relay coil current at 5 V
~ 80 mA
• 3904 rated to 200 mA
(better choice)
Q1
2N3904
V1
5V
+V
Eg. Load with 4 stages
Electromechanical Relay
R2
100
L1
R1
1k
10
Spike suppression diode
(used in parallel with any
12
inductive loads)
Image from CMU - http://www.vialab.org/Bioe_1010
2
Power output: H-bridges
Power output: H-bridge driver
The above circuits work for loads where current only travels
in one direction – how to get current to travel FORWARDS
and REVERSE?
What is the proper operation of this circuit (red = on)?
+V
Q1
1) 1 3 , 2 4 – forward
1 3, 2 4 – reverse
1 2, or 3 4 – not allowed
Q3
M1
Q2
2) 1 2, 3 4 – forward
1 2, 3 4 – reverse
1 3, or 2 4 – not allowed
Q4
3) 1 4, 2 3 – forward
1 4, 2 3- reverse
1 2, or 3 4 – not allowed
Image from wikipedia (H-Bridge)
4) 1, 2 3 4 – forward
4,1 2 3 - reverse
13
PWM on the TINAH Motor Outputs
Power output: H-bridge driver
+V
Q1
The TINAH Board has a built-in software to generate a PWM signal, and
hardware to use the PWM signal to power a small motor (max 9V, ~600 mA)
either forward or reverse.
What will happen with 1,3 OFF; 2,4 ON?
TINAH motor output schematic
Q3
1Kx5
1) Nothing – no effect on motor
M1
14
LEDs
indicate
current
direction
+5V
2) Short circuit – MOSFETS will burn
H-Bridge Chip
(SN754410NE)
Direction signal
+5V
16
Vs
3) Active braking – motor will stop quickly
4) Motor will be driven
LED5
LED1
LED6
LED2
LED7
J4
LED3
3
LED8
Q4
LED4
Q2
9V regulated
out1
out2
8
Vss
U10 cs1 1
2
in1 7 4
in2
U9b
3
SN754410NE
9 74HC04
cs2
out3
10
14
out4
in3 15
in4
U9c
gnd
6
5
4 5 1213
11
1
2
3
4
5
6
7
8
9
10
11
12
Output header
strip – note
how the pins
are grouped
6
74HC04
12
9
6
15
16
5
2
19
1Q
2Q
3Q
4Q
5Q
6Q
7Q
8Q
PWM signal (Enable)
15
TINAH motor outputs – from data sheet of on-board H-Bridge
PWM: TINAH motor outputs
TINAH/Wiring :
motor.speed(0,700);
 turn on motor 0 at ~70% duty cycle:
Red trace
H
motor
L
V
10V
Blue trace
Intermediate voltage
during high-Z state
t
17
18
3
PWM – regulated power vs. high-power
TINAH board uses a regulated 9V for each H-bridge (L78S09CV),
increased repeatability.
which remains constant under load 
HB
-1
HB
-2
STOP
(BRAKE)
lo
lo
FORWARD
hi
lo
REVERSE
lo
hi
NOT
ALLOWED
hi
hi
Some motors used in Phys 253 can use higher voltages and currents (e.g.
12V, 1.5 A) which cannot be achieved by the TINAH Board H-bridge
chip outputs directly
 use additional circuitry to control an external H
H-bridge
bridge
12V
+V
12V
+V
R7
100
12V
+V
R10
33k
Q7
2N3906
Q5
2N3904
M1
HB 1
HB-1
12V
+V
Q7
2N3906
R5
10k
R6
100
R9
33k
Q6
2N3906
Q1
Q2
MTP3055 MTP3055
H-Bridge interface
circuit
R2
100
R9
33k
Q6
2N3906
12V
+V
R6
100
TINAH Board
R10
33k
HB-1
IRF5305
IRF5305
12V
+V
R2
100
M1
Q4 Q4
MTP2955
Q8
Q
2N3904
HB 2
HB-2
12V
+V
Q5
2N3904
Q8
2N3904
12V
+V
R1
10k
Q3
Q3
MTP2955
Q3
Q4
MTP2955 MTP2955
R7
100
HB-2
12V
+V
12V
+V
R8
10k
R1
10k
R8
10k
Power output: H-bridges
R3
100
Q2 Q2
Q1Q1
MTP3055
MTP3055
HUF75321 HUF75321
R5
10k
R4
10k
R3
100
R4
10k
20
External H-Bridge
19
Power output: H-bridges
Need to connect TINAH motor outputs
to H-bridge inputs:
Build an interface circuit for doing this
To H-Bridge input
H
t
Motors
10k to 50k
Comparator level – USE 5V
FROM TINAH Board!!!
L
TINAH Motor Output
V
(do not use voltage divider, since
value decreases with decreasing
battery voltage)
10V
3V
t
21
22
DC electric motors:
DC electric motors: estimating performance
•
Sometimes you are given a graph for motor specifications,
but usually you are only given a few operating parameters:
•
•
Example motor:
torque curves
There is a linear relationship torque & speed for most small
DC motors (for geared or ungeared motors).
You can estimate a torque-speed curve using the stall torque
and no-load speed (max speed):
For Motor Power :
BaneBots, 11:1, 16mm Spur Gearmotor, FF-050
P
Operating v : 4.5v - 8v
Nominal v
: 6v
No Load RPM : 1366
No Load A
: 0.2A
Stall Current : 1.9A
Stall Torque : 10 oz-in
(72 mN-m)
Kt
: 5.4 oz-in/A (38 mN-m/A)
Kv
: 228 rpm/v
P
23
=T *
= (torque) * (ang velocity)
= 0 when T=0 or
= 0 when = 0
~ maximum when at mid-point
( ½ Tmax * ½  max)
24
Image from:
http://lancet.mit.edu/motors/index.html
4
Estimating whether or not
your motor is appropriate for the job
Info from MIT 2.007 course – a great resource!
1. Estimate desired power for the final application of the
motor (How fast does it need to go? How much force is
desired to get it to operate? How much max torque do
you need at what speed?)

Prequried = Fv
F
= T
2. Check that motor can provide adequate power (from
torque and speed specs)
3. Design a drive train to go from the motor torque/speed
to get the desired torque/speed.
25
26
http://stellar.mit.edu/S/course/2/sp10/2.007/courseMaterial/topics/topic5/resource/DCmotors/DCmotors.pdf
Gear Train / Drive Train Ratios
DC motors supplied in 253 lab
Geared Barber Coleman motor (FYQF 63310-9) (at 12V)
no-load speed: 470 rpm
max torque: 28 oz-in (20 N-cm)
no-load current: 0.1A
stall current: 1.3 A
Un-geared Barber Coleman motor (FYQM 63100-51) (at 12V):
no-load speed: 2300 rpm
max torque: 5.2 oz-in (3.7 N-cm)
no-load current: 0.13A
stall current: 2.75 A
Princess Auto Double-shaft motor (at 12V):
no-load
l d speed:
d 3700 rpm
max ttorque: 8.0
8 0 oz-in
i (5
(5.6
6 N
N-cm))
no-load current: 0.24 A
stall current: 2.2 A
Futaba Servo Motor (S3003) (motor + built-in encoder) (at 5V)
max torque: 44 oz-in torque (31 N-cm)
max speed: 0.23sec/60 degrees at no load
`
27
Gears
power in = power out
N2 teeth

Torque and speed both scale
WRT the number of teeth on
the input and output shafts.
N1 teeth
, T2
, T1
Slower = more torque.
Faster = less torque
Angular velocity:
Torque:

   
Drops in efficiency at each drive train stage are hard to estimate,
and will depend on how well things are assembled, frictional
losses, etc.
Pulley drives
•Use same ratio calculations as with gears, except use
diameters instead of teeth
• May slip, which may or may not be a good thing
(bad for accuracy, good for protection)
Spur Gears
Rack and pinion
Right-angle
g
g g
gearing
g with
bevel gears (above)
or crown gears (below)
Timing belts have beads or rubber teeth
to minimize the chance of slipping
Worm gear - lots of torque but slow
N:1 ratio (N = # teeth on spur gear)
5
12V
+V
12V
+V
12V
+V
R8
10k
L/H
OFF
ON/OFF
Q3
MTP2955
R1
10k
R2
100
R7
100
H/L
ON/OFF
12V
+V
R10
33k
H
Q5
2N3904
Q8
2N3904
HB-2
L
OFF
M1
HB-1
12V
+V
Q7
2N3906
R9
33k
Q6
2N3906
OFF
L/H
ON/OFF
R6
100
Q1
MTP3055
R5
10k
H
Q4
MTP2955
OFF
Q2
MTP3055
ON/OFF
R3
100
H/L
R4
10k
31
6