Report on electronics.

ELEC2320 - Electrical and Electronic Circuits Lab 1

• This is an assessed lab assignment.

• This lab consists of several tasks. The mark associated with each task and the corresponding marking criterion is available in a marking rubric. The marking rubric can be downloaded from the Lab Assignments sub-folder under the Course Materials folder in Blackboard.

• Please print out the marking rubric and bring that to the lab.

• For each task described below, please document your mathematical proofs, design calcula- tions, and experimental findings briefly and clearly. In addition, you will need to demonstrate the functionality of your circuit for some tasks.

• At the conclusion of each task, show your work to your lab demonstrator, and get that task marked. Please don’t forget to get your mark recorded on the marking rubric. This record should be accompanied by your lab demonstrator’s initial. Please keep this record safe in case it is needed later.

Introduction. In this lab experiment you will design and implement a simple circuit to sense a signal using a transducer. In addition you will design appropriate buffer and amplifier circuits to amplify the signal sensed. In particular, you will work with a condenser microphone, which is a capacitive sensor. Capacitive sensors of various types have enjoyed a rapid growth in popularity over the last two decades.

Condenser mic. The condenser microphone can be modeled as a (possibly nonlinear) resistor in parallel with a variable parallel plate capacitor. The distance between the plates can vary with the variation in the sound pressure. Recall that that capacitance of a parallel plate capacitor is

C = �A/d,

where A is the area of the plates, d is the distance between the plates, and � is the permittivity of the dielectric. As a result C varies when d varies. The condenser mic is connected in series with an appropriate resistor. The resistor resists flow of current into the mic. Consequently, the reciprocal of the time needed for the stored charge in C to change is at least an order of magnitude smaller than an audible frequency. As a result, the stored charge in C remains prac- tically constant, while the voltage across C varies as C varies due to variation in the sound pressure.

Circuit topology. In this lab we shall work with the non-inverting amplifier in Figure 1.

• +VCC and −VCC are the positive and negative supply voltages, respectively.

• Cd are the decoupling capacitors. These capacitors should always be incorporated when- ever we connect an active electronic component like an op-amp or a transistor to the supply rails. The decoupling capacitors stabilize the power supply voltages VCC and −VCC to prac- tically fixed values by ‘absorbing’ potentially high-frequency fluctuations in the supply rails.

1

−

+vI vO

R1

R2

−VCC Cd

+VCC

Cd

R3C1

vS

R4

VCC

mic

Figure 1: Amplifier circuit topology used in this lab.

Such fluctuations are caused by various factors like switching operations. The decoupling capacitors should be physically located as close to the op-amp supply rail pins as possible.

These capacitors are typically chosen in the order of a micro-Farad. For this simple experi- ment the decoupling capacitors may not be necessary. Nevertheless, it is a good practice to always incorporate them. This habit can save a significant amount of troubleshooting time.

• The design task is to find the values of power supply, resistors and capacitors. We shall use LM324 for this lab because it performs adequately in the audio frequency range.

Tasks.

1. In this design we like vO to swing in the range [−2, 2] volts. Recall that vO must be in the interval [−VCC,VCC]. LM324 is not an rail-to-rail op-amp, i.e. the output of LM324 saturates at a voltage below VCC in the higher side and above −VCC on the lower side.

Based on the output voltage swing specification we need to work out how much “headroom” is required on the op-amp’s power supply rails in addition to its output voltage. Often this information can be found from the relevant op-amp’s datasheet. However, LM324’s data sheet does not provide this information in sufficient detail. We shall determine the required value of VCC experimentally.

Connect one of the op-amps in LM324 as a voltage follower shown in Figure 2.

To connect an op-amp you will need to know the pinout connections of LM324 given in Figure 3.

2

−

+vi vo

−VCC

+VCC

Figure 2: Op-amp voltage follower.

Figure 3: LM324 and its pin-out connections.

Apply a triangular wave of amplitude 2V at the input (vi) of the follower, and increase VCC until vo follows vi exactly. Make sure that the frequency of the triangular wave is in between 100 Hz and 8 kHz1.

Describe your findings in a systematic way. For instance, you may document your findings in a table or a plot showing how the output amplitude changes with VCC .

For the rest of this experiment maintain VCC at the value obtained in this step.

2. Build the circuit in Figure 4, where you take a range of different values of R4 between 1 to 15 kΩ.

Examine the waveform of vS (the signal vS is marked in the circuit diagram). You will shortly see that we can express vS as

vS(t) = VS + vs(t),

where VS is a DC offset, and vs(t) is a time-varying audio signal picked up by the mic. The amplitude of vs(t) can be much much smaller than VS (so small that vS(t) may appear constant in an oscilloscope.)

1You may like to investigate how the follower output deviates from the ideal output if you increase the frequency beyond audio range. This is a simple way to experience the gain-bandwidth limitation of an op-amp. The gain- bandwidth product of LM324 is about 1MHz. Under the voltage follower configuration the gain is unity. Hence one expects to see the gain-bandwidth product limitation around and above 1 MHz.

3

vS

R4

VCC

mic

Figure 4: Connection of the mic in series with resistor R4.

Examine how VS varies as we change R4. Choose a suitable value of R4 such that VS is somewhere between 0.5V to 1V.

Describe your findings in a systematic way using a table or a plot. What do you conclude about the behaviour of the mic from this experiment? Can you explain why it is not a good idea to set VS near VCC (think about power consumption)?

3. Consider the voltage divider formed by the mic and R4 in Figure 4. This voltage divider acts as the source to the series combination of R3 and C1 in Figure 5.

For the voltage divider in Figure 4, estimate the Thevenin’s equivalent resistance RTh between the terminals of the mic for your choice of R4. For this neglect the capacitor inside the mic. In this way, we shall over-estimate the Thevenin’s equivalent impedance.

Take R3 (see Figure 5) at least 10 times higher than RTh. Do you see why? Observe that the series combination of R3 and C1 in Figure 5 acts as a load to the voltage divider in Figure 4. We must ensure that the load impedance is significantly larger than the internal resistance RTh of the source formed by the voltage divider.

4. Analyze the circuit in Figure 5.

Use the Thevenin’s equivalent model derived in the previous task. Considering R3 � RTh, show that if vs is a sinusoid of angular frequency ω, then vI is a sinusoid of frequency ω, and in addition,

~vI = jωC1R3

1 + jωC1R3 ~vs

What is the voltage across C1? This might be a little tricky. Use Superposition theorem. Note that ~vI is the phasor associated with vI , and ~vs is the phasor associated with vs. Choose C1 such that vI ≈ vs for all frequencies between 100 Hz and 8KHz. For that you need

1 � ωC1R3, for 200π ≤ ω ≤ 16000π.

5. Bring a sound source near the mic. Make sure the sound intensity is adequate. Measure the amplitude of vI in the oscilloscope. Calculate the gain of the non-inverting amplifier in

4

vS

R4

VCC

mic

C1

vI

R3

Figure 5: The DC blocking capacitor C1 and R3 connected at the output of the voltage divider in Figure 4.

Figure 1 so that the amplitude of the output vO in Figure 1 is 2V. Choose R1 and R2 to provide the gain needed. While choosing R1 and R2 ensure that

• R2 don’t dissipate more than 0.1 watt, • R1 don’t dissipate more than 0.1 watt, • The peak current supplied by the op-amp is below 5mA.

6. Implement the amplifier as per your design. Demonstrate that it performs as per the speci- fication.

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