12B: Inverting amplifier

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12B: Inverting amplifier#

Learning goal: Calculate and explain some properties of an inverting amplifier circuit. Build the circuit and observe it in real life.

Structure of an experiment:

Background+Anticipate+ Simulate(5+20+10 min): per person
Implement + Investigate (60 min): with your partner (group of 2)
Compare + Conclude (15 min): with a group of 4 (per table)

Extra information or hints is given in boxes denoted by: ℹ️
Help fixing progrems is given in boxed denoted by: 🔥

Materials used:

Alpaca
opamp TL072
220 and 1k \(\Omega\) resistors

BACKGROUND#

⏳ Estimated time: 5 min

Below is an inverting amplifier circuit is depicted

In the above circuit, the + (non-inverting) input is connected to ground. Because of (ideal) opamp characteristics, the - (inverting) input will be a virtual ground point.

In an ideal opamp, the voltage difference between the inverting and non-inverting inputs is virtually zero. Thus, if the non-inverting input is grounded, the inverting input also appears to be at ground potential, even though there is no physical connection to ground.

Due to the virtual ground, the voltage across \(R_b\) is \(V_{source}\), and the voltage across \(R_a\), it is \(V_{out}\), so (as per Ohm’s law) the current through \(R_b\) and \(R_a\) is equal.

ℹ️ Hints

The current through \(R_b\) will be \(\frac{V_{source}}{R_b}\). The current through \(R_a\) is \(V_{out}\) times \(R_a\), but with a minus sign.
The sign change is due to \(I=(V_{in}-V_{virtual ground})/R_{b} = (V_{virtual ground}-V_{out})/R_{a}\).

Can you now calculate the gain?

ANTICIPATE:#

⏳ Estimated time: 20 min

Calculate the gain of the above circuit. Clearly state the formula you used to calculate the gain.

### TO DO="# write your answer here: gain formula+ calculation"

If you apply a sine between 0 and 1 V, what would be the Vout?
Reason whether you can directly measure this Vout with the analog Input Pin.
In doubt: check with your TA before connecting, and always use the Voltmeter on the Cria first.

### TO DO="# write your answer here: Vout + safe to connect?"

If the operational amplifier is assumed to be ideal, what are the input and output impedance?

### TO DO="# write your answer here: input and output impedance opamp"

SIMULATE:#

⏳ Estimated time: 10 min

Recreate the above inverting circuit in LTSpice, and observe Vin and Vout. Are they indeed inverting?
Use the same simulation settigns as in 12A. Remember to power the opamp!
Upload the screenshot of the graph and you setup.

from ipywidgets import FileUpload
from IPython.display import Image
import os
upload=FileUpload()
upload

file_name="12B_1_inverting_input.jpg"
if upload.value!={}:
    with open(file_name,"wb") as f:
        try: f.write(upload.data[-1]) # python 3.7 Kernel code, not working on Vocareum
        except: f.write(upload.value[-1]["content"])  # python 3.8 Kernel code, not working on Vocareum

Image(filename=file_name, width="50%")

Precap video: https://www.youtube.com/watch?v=i8DNapKYyXQ

IMPLEMENT & INVESTIGATE:#

⏳ Estimated time: 60 min

You will be building an measuring the characteristics of the inverting amplifier using the ALPACA.
The pin diagram of the operational amplifier is given below as reminder:

The non-inverting input is marked with a (+)
and the inverting input with a (-).

Exercise 1: build an inverting opamp circuit#

📝 Todo:

Build the inverting amplifier circuit as depicted below

Measure both the input signal that is generated with DAC output A, and the output of the opamp.
Use the amplifier (AMP1 IN and AMP0 IN pins) for measuring the analog signals, since these pins are protected against too high voltages.
Connect the jumpers using the illustration below. This setup will not change the input signals, but simply protects the PicoPi.
Remember to power your opamp!

ℹ️ Hints : Instead of using a jumper at AMPLIFIER DIRECT TO NANO, consider using a wire to bridge the connection instead. It is easier to place and remove!

ℹ️ Hints Fritzing circuit

Your circuit should look somewhat like the built circuit below. Remeber that resistors in the image might not have correct colors. Note the jumpers in pink.

The code for this exercise has already been written and can be found below. The code generates a sine wave at 50 Hz with a \(V_\text{PP}\) of 0.5 volt with Vmin = 0.

🔥

Before running the code, please verify that:

Both USB cables are plugged in

The +12 V and -12 V switches are turned to the on position on the ALPACA.

Resistors are in correct position! - doublecheck if they are correctly placed in relation to the inputs and outputs of an opamp

Try to predict what the output will look like.

### TO DO="# the predicted output voltage"

# Run this cell to connect your ALPACA
%serialconnect to --port="COM3"
#ADD COM PORT ABOVE, e.g. --port="COM3"

import time
import numpy as np
import matplotlib.pyplot as plt
from machine import ADC # type: ignore
from functiongenerator import FuncGen, Sine # type: ignore

# Do you know what these variables define?
NUM_SAMPLES = 200
DELAY_MS = 1 # Sampling delay in ms

# How would you figure out which ADC(??) ports to use?
adc0 = ADC(26)
adc1 = ADC(27)

# Remember to initialize the arrays to store the acquired data
input_signal = np.zeros(NUM_SAMPLES) #arrays
output_signal = np.zeros(NUM_SAMPLES)

# Define the procedure for the function generator and the acquisition
with FuncGen(Sine(Vmax=0.5, Vmin=0, freq=50)):
    time.sleep_ms(1000)
    for ii in range(NUM_SAMPLES):
        input_signal[ii] = adc1.read_u16()
        output_signal[ii] = adc0.read_u16()
        time.sleep_ms(DELAY_MS)

# Convert integer input/output signal to voltage.
input_signal = input_signal / 65535 * 3.0
output_signal = output_signal / 65535 * 3.0
print(np.max(input_signal), np.max(output_signal))
print('Aquisition done!')

No serial connected
  %serialconnect to connect
  %esptool to flash the device
  %lsmagic to list commands

# Plot
plt.plot(input_signal, label='Input signal')
plt.plot(output_signal, label='Output signal')
plt.ylabel('signal [V]')
plt.xlabel('Measurement number')
plt.legend()

print('Plotting done!')

# Calculate Vpp for input/output and gain
Vpp_input = np.max(input_signal) - np.min(input_signal)
Vpp_output = np.max(output_signal) - np.min(output_signal)
gain = Vpp_output/Vpp_input

# Print the results of the calculations
print(f'The Vpp of the input signal is: {Vpp_input:.2f} V')
print(f'The Vpp of the output signal is: {Vpp_output:.2f} V')
print(f'The gain is {gain:.2f}')

Exercise 2: No detectable output signal??#

Explain why you do not detect an output signal?

ℹ️ Hint 1 : To see if there is any output generated by the opamp, connect the signal at the output of the opamp to the voltmeter on the Cria. Lower output the frequency of the DAC to 1 Hz and observe the indicator leds. Do not forget to change the frequency back when you continue to the next question.

ℹ️ Hint 2: Think about Alpaca’s limitations

### TO DO="# write your answer here: why don't you get an output signal?"

Exercise 3 Influence AC-DC coupling on output signal#

Measure the output of the opamp both in AC and in DC coupling for AMP0 IN.

Just like the in 12A, we can use the amplifier on the ALPACA to visualize signals which we could otherwise not observe.
Similar to the scope in the studio classroom, we can switch between AC and DC coupling mode.

📝 Todo:

Use the jumper closest to the SIGNAL+ pins of the amplifier to switch the AMP0 IN amplfier between the AC/DC coupling modes.
- Note that this corresponds to the top jumper in blue circle in the illustration above showing the jumper settings.
- Having the jumper on the pins sets the input to DC coupling, whilst having it off sets the input to AC coupling.

PART 1 - AC/DC coupling#

A) In which mode do you see the signal?

B) Deduce why AC and DC coupling result in their corresponding signals.

### TO DO="# write your answer here: influence AC and DC mode"

C) Why does the signal appear to have a 180 degree phase shift compared to the input signal?

### TO DO ="# write your answer here: explain phase shift"

You can use one more trick to visualize the output signal more clearly. You can apply a DC offset to the output signal before measuring it.

PART 2 - DC offset#

📝 Todo:

For this purpose connect a jumper over the pins called: WITH OFFSET, on the amplifier corresponding to AMP0 IN. See the image below for the correct jumper settings.
The jumpers for AMP1 IN should not be changed.
Put AMP0 IN in DC coupling mode again.

The potentiometer above AMP0 IN can now be used to regulate the DC offset that is added to the signal.
Regulate the DC offset of the signal such that the entire output signal can now be visualized. To make it easy to find the right setting for the potentiometer, you can use a special plotting mode unique to NB2211 that allows you to plot the data live.
This function is called plt.liveplot. When a number is put into plt.liveplot, e.g. plt.liveplot(x), the value x will be added as a point on the plot. Note: this only works if the cell containing plt.liveplot starts with the “magic command” %plot --mode live

📝 Todo:

Use the live plot to acquire the full signal. Turning the potentiometer clockwise will increase the DC offset, turning it counter-clockwise will lower the DC offset.
- The range is finicky, so you will need to adjust carefully
Measure the gain using the (non-live) code you used at Exercise 2.

%serialconnect to --port="COM3" 
#ADD COM PORT ABOVE, e.g. --port="COM3"

%plot --mode live

import time
import numpy as np
import matplotlib.pyplot as plt
from machine import ADC # type: ignore
from functiongenerator import FuncGen, Sine # type: ignore

# Instantiate two measurement pints, one for Ain0 the other for Ain1 to measure the input and output signal
adc0 = ADC(26) 
adc1 = ADC(27)

with FuncGen(Sine(Vmax=0.5, Vmin=0, freq=1)):
    
    time.sleep_ms(100)
    
    for ii in range(400):
        input_signal = adc1.read_u16()
        output_signal = adc0.read_u16()
        input_signal = input_signal / 65535 * 3.0
        output_signal = output_signal / 65535 * 3.0
        plt.liveplot(input_signal , output_signal, labels = ['Input', 'Output'])
        time.sleep_ms(100)

Exercise 4: Measure + evaluate the gain#

THINK:

Use the new knowledge from the setup in exercise 3.
Do you need to put back the jumper to switch from AC and DC coupling mode?
When fine tuning the offset, what should you bear in mind about the lower and the upper limit of the observed signal?

Now:

A) Measure the gain (use non-live code from ex 2)

B) Reflect back on the answer you gave in Exercise 3C, was this answer correct?

### TO DO="write your answer here: measured gain + reflection"

This opamp circuit you built can be used to amplify signals, as you saw during this exercise, but it can also be used to attenuate signals. This attenuation is similar to the amplifier circuit we used in the non-inverting opamp exercise to measure the clipped signal. Attenuating a signal is useful because the PicoPi can only measure voltages from 0 to 3.0 volt. By attenuating a signal, we can measure voltages over a larger voltage range.

Exercise 5: Adapt resistors for another gain value#

PART 1 - adapt#

How should the resistors be changed to attenuate the signal with a factor of 4.5?

### TO DO="# write your answer here: how to attentuate"

Implement the circuit you just suggested

📝 Todo:

Keep the jumpers on the ALPACA amplifier AMP0 IN unchanged
Remove the wire connecting AMP1 IN. It will not be used.
Remove the jumper for ADC1 at AMPLIFIER DIRECT TO NANO.
Instead of using the output from DAC A directly, use the DAC ASSISTANT.
- Connect a wire from DAC output A to the +IN pin of the DAC assistant.
- Connect the output from the OUT pin of the DAC assistant to the input of the opamp circuit
Select the resistors based on your answer.

ℹ️ Hint on the circuit

: your circuit should look somewhat like the built circuit below. Note the jumpers in pink. Remember that resistors shown on the graphic might not be correct. > >

The signal generated at the output of the DAC assistant now has an amplitude running from +4.8 to -4.8 V. This 9.6 volt peak to peak amplitude is too large to measure directly with the PicoPi, so we need to attenuate it first. This should be done using your opamp circuit.

PART 2 - adapt#

📝 Todo:

Acquire the entire signal generated using the live plotter below
Observe whether you can still use the offset knob. Do you need it?
Perform the measurement and find the gain using the code below.

Live plotter:#

%serialconnect to --port="COM3" 
#ADD COM PORT ABOVE, e.g. --port="COM3"

%plot --mode live


import time
import numpy as np
import matplotlib.pyplot as plt
from machine import ADC # type: ignore
from functiongenerator import FuncGen, Sine # type: ignore

# Instantiate two measurement pints, one for Ain0 the other for Ain1 to measure the input and output signal
adc0 = ADC(26) 

with FuncGen(Sine(Vmin=1.1, Vmax=3, freq=1)):
    
    time.sleep_ms(100)
    
    for ii in range(200):
        output_signal = adc0.read_u16()
        output_signal = output_signal / 65535 * 3.0
        plt.liveplot(output_signal, labels = ['Output'])
        time.sleep_ms(100)

Final acquisition:#

import time
import numpy as np
import matplotlib.pyplot as plt
from machine import ADC # type: ignore
from functiongenerator import FuncGen, Sine # type: ignore

# ACQUISITION SETTINGS
NUM_SAMPLES = 350
DELAY_US = 500 # Sampling delay in us

adc0 = ADC(26) 

output_signal = np.zeros(NUM_SAMPLES)

with FuncGen(Sine(Vmin=1.1, Vmax=3, freq=50)):
    
    time.sleep_ms(100)
    
    for ii in range(NUM_SAMPLES):
        output_signal[ii] = adc0.read_u16()
        time.sleep_us(DELAY_US)
        
# Convert integer input/output signal to voltage.
output_signal = output_signal / 65535 * 3.0

print('Aquisition done!')

# Plot
plt.plot(output_signal, label='Output signal')
plt.ylabel('signal [V]')
plt.xlabel('Measurement number')
plt.legend()

print('Plotting done!')

# Calculate Vpp for input/output and gain
Vpp_input = 9.6
Vpp_output = np.max(output_signal) - np.min(output_signal)
gain = Vpp_output/Vpp_input

# Print the results of the calculations
print(f'The Vpp of the input signal is: {Vpp_input:.2f} V')
print(f'The Vpp of the output signal is: {Vpp_output:.2f} V')
print(f'The gain is 1/{1/gain:.2f}')

Exercise 6: Measure full sine wave with Alpaca’s on-board amplifier#

A) Are you able to detect the entire sine wave?

B) Comment on why using the amplifier on-board the ALPACA is still necessary for this measurement.

### TO DO="# write your answer here: able to measure full sine, and is amplifier still necessary?"

COMPARE & CONCLUDE#

⏳ Estimated time: 15 min

Wait till 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:

Discuss the various ways that one can measure a purely negative signal on the PicoPi. Which method will lead to what results?

A. Directly on Analog in hypothetically
B. Via AC/DC coupling of the amplifier
C. with offset of the amplifier

Discuss why at Exercise 6 you still need the amplifier, although the \(V_\text{PP}\) is in range of the PicoPi
exit card:
1. Write a brief abstract on what you learned (conclusion, useful graph),
2. Which troubleshooting skills do you want to remember for next sessions,
3. Which code do you copy for use in next sessions,
How do you think this notebook could be improved?

#12B inverting opamp
### TO DO ="1. discuss the various ways to display a negative signal by the alpaca"

### TO DO ="2. why do you need an amplifier in exercise 6?"

### TO DO="3a. abstract"

### TO DO="3b. troubleshooting"

### TO DO="3c. code"

### TO DO="4. what changes would you suggest?"

Recording: https://www.youtube.com/watch?v=hR9duxRafQ4

12B: Inverting amplifier

Contents

12B: Inverting amplifier#

BACKGROUND#

ANTICIPATE:#

SIMULATE:#

IMPLEMENT & INVESTIGATE:#

Exercise 1: build an inverting opamp circuit#

Exercise 2: No detectable output signal??#

Exercise 3 Influence AC-DC coupling on output signal#

PART 1 - AC/DC coupling#

PART 2 - DC offset#

Exercise 4: Measure + evaluate the gain#

Exercise 5: Adapt resistors for another gain value#

PART 1 - adapt#

PART 2 - adapt#

Live plotter:#

Final acquisition:#

Exercise 6: Measure full sine wave with Alpaca’s on-board amplifier#

COMPARE & CONCLUDE#