%python
from IPython.core.display import HTML
def set_width(width):
display(HTML(f"""<style>
.container {{ width:{width}% !important;
min-width:800px !important; margin: 0 auto}}
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set_width(50)
4B: RC circuit with PicoPi#
Learning goal: Build the RC circuit and determine the time constant
Structure of an experiment:
Anticipate + Simulate (10+10+10): per person. This is homework and should be finished before you start your 4 hours practicum session
Implement + Investigate (30+10): with your partner(group of 2)
Compare + Conclude (5 min): with a group of 4(per table)
Extra information or hints is given in boxes denoted by: ℹ️
Help in fixing problems is given in boxed denoted by: 🔥
Materials used:
Alpaca
22kΩ resistor
220 nF capacitor (big orange)
BACKGROUND: Alpaca#
⏳ Estimated time: 10 min
Below are two videos that you have already seen in 3A. Watch them if you want to review the topic.
ℹ️
Notice that in Anticipate there is a different RC filter used.
ANTICIPATE: RC circuit 3dB point#
⏳ Estimated time: 10 min
For the circuit above:
Derive the type of filter
Calculate the cut-off frequency and time constant
### TO DO="your answer, type of filter, cut-off frequency and time constant"
SIMULATE: RC circuit 3dB point#
⏳ Estimated time: 10 min
You can download the file called “4_RC_CR_RCCR_Simulate” which should contain an RC circuit that looks like this:
You can run this simulation and by right-clicking on the voltage source you can see that you are performing an AC Analysis. This varies the frequency between 1kHz-10kHz such that you can plot Vout to find the -3dB point.
ℹ️
The graph plots dB against Hertz. You can determine the frequency by clicking on the name on top of the graph. Also remember that omega=2pi*f
### TO DO="What frequency does the -3dB point occur at"
You will implement the circuit, do measurements and analyze them. The assignment is broken into two steps:
Implement the circuit and acquire data
Investigate, by analyzing the acquired data
IMPLEMENT&INVESTIGATE 1: Step function#
⏳ Estimated time: 30 min
You will build the RC circuit as below on your Alpaca (220nF is the big flat red capacitor):
📝 Todo:
Connect the input of the RC circuit (\(V_{in}\)) to Dout0
Connect the input of the RC circuit (\(V_{in}\)) to Ain0 on the multifunction connector (Pin 26)
Connect the output of the RC circuit (\(V_{out}\)) to Ain1
Connect the circuit the the ground, on the bottom of your Alpaca
ℹ️ Hint for implementation on the Alpaca
We will now use a script that:
Takes 50 samples of the output signal, while the input signal generated by Dout0 is 0V.
After these 50 measurements, the voltage of Dout0 is put to 3.0V, and 450 additional samples of the output are performed.
For each measurement, the time at which the measurment was performed is recorded.
The measured output versus the time is plotted.
ℹ️ To keep track of when each measurement was taken, consider the following approach:
Record the time at the start of the measurement.
Store the time at the start of your measurement in a variable
start.Each time you measure, check the time again. Subtracting this time from the start time will yield the time elapsed since the start of the measurement!
What do you think will be more reliable: an array that interpolates between the start time and the end time or the measured time?
How to do this in MicroPython: As you are measuring using a delay of just 4 milliseconds, you might want to meausure these times in milliseconds too, rather than full seconds. To do this, use
time.ticks_ms. This gives a “time” in milliseconds. Explore how this works in the code below. Equivalently, instead oftime.sleep, you can also usetime.sleep_msto specify a time to sleep in milliseconds.
First change the COM port in the code below and run the code of the next cell.
%serialconnect to --port="COM4"
#### Explore measuring time points in milliseconds using this code ####
# if you want to explore, change the code from if 0: to if 1:
import time
if 0:
start = time.ticks_ms() # Current time measured in milliseconds
tt = [] # List to store time points
for ii in range(600):
tt.append(time.ticks_ms() - start) # Store time
time.sleep_ms(4) # delay
print(tt[0:50]) #do you see multiples of 4 ms?
The code is already given to you, you don’t have to write it yourself. All you have to do is run it. If you want to get more indepth explanation of the code, feel free to watch the movie below.
from machine import ADC, Pin
import time
import matplotlib.pyplot as plt
import numpy as np
from functiongenerator import FuncGen, DC
Ain0 = ADC(26) # Pin 26, Vin
Ain1 = ADC(27) # Pin 27, Vout
from machine import Pin
Dout = Pin(14, Pin.OUT)
#define the arrays to store data, and activate the pins
Nm = 200 #number of measurements
samples_OUT = np.zeros(Nm, dtype=np.uint16)
samples_IN = np.zeros(Nm, dtype=np.uint16)
tt = np.zeros(Nm, dtype=np.uint16)
print("Starting the measurement\n")
start = time.ticks_ms() # Current time measured in milliseconds
for ii in range(Nm):
samples_OUT[ii]=Ain1.read_u16() # Take a sample
samples_IN[ii]=Ain0.read_u16() # Take a sample
tt[ii]=time.ticks_ms() - start # Store time
time.sleep_ms(1)
if ii == 50: # Do this once, and don't forget to turn it off once the loop ends
Dout.value(True)
print(ii, "samples acquired\nEnabling Dout0 (Pin GP14)\n")
Dout.value(False)
tt = np.array(tt) # Convert to Numpy array for easy operations
samplesOUT = np.array(samples_OUT)
samplesIN = np.array(samples_IN)
plt.plot(tt, samplesOUT * 3.0 / 65535, '.-', color='b', label='V_out')
plt.plot(tt, (tt > tt[50]) * 3.0, '.-', color='r', label='V_in Theoretical')
plt.plot(tt, samplesIN * 3.0 / 65535, '.-', color='g', label='V_in')
plt.xlabel("Time [ms]")
plt.ylabel("Voltage [V]")
plt.legend()
print(Nm, "samples acquired\nDisabling Dout0\n\nMeasurement is done!")
IMPLEMENT & INVESTIGATE 2: Time constant#
⏳ Estimated time: 10 min
Above, you have made a plot of the data. We can now determine the time constant \(\tau \) experimetaly. Fill in the missing threshold value (???) in the code below to calculate the time constant automatically and print the value to the console.
ℹ️ Hint
The time constant is the time it takes until the signal reaches about \(e^{-1}\) of its maximum value. You can also think about this as a timepoint when the Vout is equal to e\(^{-1} V_{max}\). When you input the threshold into the code, it will find for you that timepoint.
voltages= samples_OUT * 3.0 / 65535
idx = np.argmax(voltages) # Index where voltage drop starts, argmax returns the first for multiple maxima
tt_start = tt[idx]
voltages_clipped = voltages[idx:]
tt_clipped = tt[idx:]
#Calculate time constant automatically
'''
Write code here, including defining a threshold=???? in order to find the crossing with that threshold.
Think about capacitor discharge time and realise you want to find tau=RC, and input the correct formula accordingly as a threshold
Hint: Remember the voltage that was set
'''
### TO DO="threshold =???, #for you to fill in"
tt_37_percent = tt_clipped[np.argmax(voltages_clipped < threshold)] # get first value where sample > threshold, check out np.argmax
tau = tt_37_percent - tt_start
print(f"The time contant is {tau} miliseconds.")
plt.plot(tt_clipped, voltages_clipped, '.-', color='b', label='V_out [V]')
plt.vlines(tt_start, 0, 3.0, color='grey', label='Dout0 is ON [ms]', linestyle='dashed')
plt.vlines(tt_37_percent, 0, 3.0, color='grey', label='Threshold reached [ms]', linestyle='dashed')
plt.hlines(threshold, tt_clipped[0], tt_clipped[-1], color='magenta', label='Threshold [V]', linestyle='dotted' )
#plt.hlines(threshold, tt_clipped[0], tt_37_percent, color='black', label='RC Time', linestyle='solid' )
plt.xlabel("Time [ms]")
plt.ylabel("Voltage [V]")
plt.legend()
print('Summary of the measurement:\n')
print('Samples 50 to 60 acquired from Dout0 [V]:',voltages[50:60])
print('Associated timestamps [ms]:',tt[50:60], '\n')
print('Index of the first sample when Dout0 is enabled:', np.argmax(voltages==np.max(voltages)))
#print('Index of the sample with the (first) recorded maximum value:', np.argmax(voltages))
print('Time when Dout0 is enabled [ms]: ', tt_start)
print('V_out when Dout0 is enabled [V]: ', voltages[np.argmax(voltages==np.max(voltages))], '\n')
print('Threshold value [V]: ', threshold, '\n')
print('Index of the sample with the measurement below the threshold: ', int(np.argmax(voltages==np.max(voltages))+np.argmax(voltages_clipped < threshold)))
print('Time from start when threshold is reached [ms]: ',tt_37_percent)
threshold_index = int(np.argmax(voltages==np.max(voltages))+np.argmax(voltages_clipped < threshold))
print('V_out when the threshold is reached [V]: ', voltages[threshold_index], '\n')
print(f"The time contant is {tau} miliseconds.")
Do not remove this circuit from your Alpaca, you will need it in the next assignment!!
COMPARE & CONCLUDE (first within your group, then with the TA)#
⏳ Estimated time: 5 min
Wait until all (4) group members finish their observation
Compare your results with your other group members.
If your results agree, and are in line with all predictions, then talk to a TA and get checked off
Otherwise, so if your results do not agree, or your results are not in line with your predictions, then first discuss amongst your group before getting a TA.
to be checked off by a TA:
What is the value of the cut-off frequency?
How does the calculated time constant compare to the theoretical value? Please explain the (expected) difference.
exit card:
Write a brief abstract on what you learned (conclusion, useful graph),
Which troubleshooting skills do you want to remember for next sessions,
Which code do you copy for use in next sessions,
How do you think this notebook could be improved
This notebook is on your laptop. To complete the opportunity for TA+teachers, upload this notebook again into Vocareum + submit
### TO DO="1. cut-off frequency"
### TO DO="2. comparison calculated with theoretical time constant"
### TO DO="3a. abstract"
### TO DO="3b. troubleshooting"
### TO DO="3c. code"
### TO DO="4. what changes would you suggest?"
%rebootdevice
%disconnect
If you got stuck during the measurement, at the end of the lab assignment we offer you a movie clip with our recorded efforts in the lab. If you were successfull with measuring, then skip this movie clip