1/31 Lab 2: Thevenin's Good Idea

in which Julia compares voltage in Thevenin-modeled circuits

Our first task: connect a LEGO motor directly between the power and ground busses and feel the torque on the motor under stall conditions.

Next, we monitored voltage between power and ground with and without the motor connected.  We saw no change in voltage when the motor was plugged in--the oscilloscope read a constant 2.0 V. (The Thevenin model then suggests that the resistance in the motor is much larger than the resistance in the battery.)

We repeated this exercise with voltage from Output 1 of the LogoChip.  When manually stalling, we felt slightly less torque than when the motor was powered by the battery.  The voltage did change in this scenario: there was slightly less voltage when plugged in (about 3.8 V), oscillating at about 300 Hz (we think as the motor disconnects and reconnects to the voltage source as it spins to continue motion in the same direction when fed direct current; note that this is much greater than the frequency of motor arm spin, both because of gearing and because the motor disconnects/reconnects several times per revolution).  Upon manual stalling, the oscilloscope showed a flat line at slightly higher voltage (4.0 V).  The noticable change in voltage suggests that the resistance in the LogoChip is significant compared to the resistance in the motor.

A circuit to monitor the motor attached to the LogoChip.

Next we used the oscilloscope to monitor the change in voltage between power and ground busses (Vp) as we connected and disconnected a 47 Ω resistor, to approximately calculate the Thevenin equivalent circuit for the battery pack.
         When no resistor or a 47 Ω resistor* was inserted into the circuit, the voltage was a constant 3.3 V.  With a 15 Ω resistor, the voltage decreased to a constant 2.2 V.
         Vout = (R1/(R1+R2))*Vin
         2.2 = 15*3.3/(R + 15) so R+15 = 13*3.3*2.2 so R = 13*3.3*2.2 - 15 = 7.5 Ω.
Thus the battery pack can be modeled by the Thevenin equivalent circuit of a voltage source of 2.2 V and resistor of 7.5 Ω.
*(I'm not convinced that any circuit would show no voltage change with no added resistor and a 47 Ω added resistor but change at a resistance somewhere in the middle (15 Ω)--I would expect the 47 Ω resistor to show a much more pronounced effect than the 15 Ω resistor.  I suspect I incorrectly inserted the 47 Ω resistor in this circuit.  However, the same analysis should work with a 15 Ω resistor.)

Then we used PicoBlocks to set one LogoChip output pin "high", and measured the change between voltage and ground with the 47 Ω resistor to calculate its Thevenin equivalent circuit. 
         No resistor: 3.3 V
         47 Ω resistor: 1.0 V
         Vout = (R1/(R1+R2))*Vin
         1.00 = 47*3.3/(R+47) so R = 47*3.3*1.0 - 47 = 108.1 Ω.
Thus the Thevenin equivalent circuit of this LogoChip is a voltage source of 1.0 V with a 108.1 Ω resistor.

Next we determined the Thevenin equivalent resistance (Rth) for nonspinning LEGO motor and calculated how much current really flows into a motor driven by a LogoChip pin.  The oscilloscope showed 0.6 V flowing through the motor when manually stalled.
         Vout = (R1/(R1+R2))*Vin
         0.6 = (R/(R+108.1))*3.3 so 0.6*R + 108.1*0.6 = 3.3*R so R = 108.1*0.6/2.7 = 24.02
Thus Rth = 24.02 Ω for the motor.
For a nonspinning motor: V = 0.6 V, R = 24.02 Ω, so I = V/R = 0.6/24.02 = 0.025 A or 25 mA
Thus for a stalling motor driven by a LogoChip pin, about 25 mA of current should flow.  This calculated value agrees with the literature--a LogoChip pin should output about 25 mA of current.

The oscilloscope measuring a motor running on LogoChip voltage: variable at about 3 V.

The oscilloscope measuring a stopped motor on LogoChip voltage: flatline at about 0.6 V.

Finally, we completed Lab 1-4 in Horowitz & Hayes' Student Manual for the Art of Electronics.
We connected a 10 kΩ resistor in series with a battery pack (Vin = 4.2 V), measured the output voltage (open circuit voltage = 2.4 V), then added another 10 kΩ resistor in series as a load.  The new output voltage was 1.6 V.  Next we shorted the output to ground to measure the short circuit current (Isc): although we could not find an ammeter to accurately measure such a small value, when loaded the Isc was about 1 mA.  From this we concluded that the Thevenin resistance was (1.6 V / 0.001 A = ) 5 kΩ.

We used a variable voltage source (a function generator) to create and test the Thevenin equivalent circuit:
Vin = 2.4
Rth = 4.7 kΩ (about 5--we had no 5 kΩ resistor)
Rload = 10kΩ

The variable voltage source (function generator) we used to input 2.40 V.

The Thevenin equivalent circuit for Lab 1-4.

We measured 2.4 V across the first resistor and 1.6 V when loaded with 10 kΩ resistor, showing that this is indeed a Thevenin equivalent circuit to the 10kΩ + 10kΩ + 4.2 V original circuit.


Next lab: More with the Digital Oscilloscopes and AC Voltage Divider, Experimentally!