ELEC 243 Lab

Experiment 6.1

Transducer Amplifiers

The voltage amplifiers from the previous Experiment can be used to amplify the output of a transducer which produces a voltage or to drive the input of one which accepts a voltage. Indeed, that's just what we did in Part 2. However, some of our transducers produce or accept things other than voltages. We currently have a handle on resistive transducers, although we will get a better one in subsequent Labs. Let's now direct our attention to another class of transducers in our parts kit: the photodiode and the LEDs.

We tried connecting these devices directly to our measuring instruments in Experiments 1.2 and 2.4 with less than ideal results. The reason for this is their performance is based on current rather than voltage or resistance. We have no signal source which produces current as an output (to drive the LED) and our current measuring equipment is not sensitive enough to produce useful readings from the photodiode.

In this Experiment, we will use op-amps to produce a pair of hybrid amplifiers. One is an amplifier which accepts a current as an input and produces a voltage as an output. Quantitatively we can express this as $v_{out}=R_mi_{in}$ where $R_m$ is the gain of the amplifier. $R_m$ is called the mutual resistance or more commonly transresistance (short for "transfer resistance"). Similarly a transconductance amplifier will convert an input voltage $v_{in}$ to an output current $i_{out}$ according to $i_{out}=G_mv_{in}$ .

There is a variety of applications for either a transresistance amplified photodiode or a transconductance amplified LED. A further set of applications is opened up by combining the two into an emitter-detector pair. We saw one such application in Part 4 of Experiment 2.4 where we built a miniature optical communication system using an LED as a transmitter and a photodiode as the receiver. In a communication system we want to maximize the achievable distance between transmitter and receiver and our main concern about the space between them is that it cause as little attenuation to the transmitted signal as possible.

Another class of applications precisely fixes the transmitter and receiver and attempts to deduce information about the material between them by measuring the attenuation. Any actual information transmitted is purely incidental. We will examine some of those applications in subsequent labs. Today we will assemble the components into a convenient, mechanically stable package and provide additional circuitry to improve the linearity and sensitivity of the resulting emitter-detector pair.

Part 1: An Emitter-Detector Pair

For a communication system portability of the transmitter and receiver is important. However, many of the measurement systems based on optical emitter-detector pairs require a precisely fixed physical relationship between the transmitter and receiver. Our first step will be to build the mechanical structure to define that relationship.


Opto-Mechanical Components:

 As we saw in Experiment 2.4 careful and steady alignment between transmitter and receiver (LED and photodiode) is essential for a consistent received signal. Since the measurements we want to make depend on detecting very small changes in received signal strength, it's clear that holding the LED and photodiode by hand will not be satisfactory.

By a lucky coincidence, the holes in Lego pieces are almost exactly the right size for the photodiode and non-jumbo LEDs. Although their rigidity leaves something to be desired, it is adequate for our purposes and much better than holding by hand. Also, the ease with which assemblies may be constructed and modified means that we can finish this lab much faster than if we had to machine each mounting structure out of a block of titanium.

For maximum flexibility, we will use the smallest lego piece with a suitable hole, the 1x2 beam, to mount the photodiodes and LEDs. We have a number of different LEDs available including red, green, yellow, blue, and white. For convenience you can mount each LED in its own block. The blocks are available in assorted colors, so you can color-code the block to match the LED to make selection easier. For today we will only be using the small high-brightness red LED, so if you are in a hurry you need only make up one LED block. Press each LED firmly (but not too firmly, as you will eventually have to remove it) into the hole in a 1x2 beam. The leads should be arranged parallel to the long axis of the block:

Although the LEDs are a nice, snug fit in the Lego holes, the photodiode is a bit too small and will fall out without assistance. We can fix this problem, and provide a bit of shielding from stray light, by the following procedure: Cut a strip of black paper 7 mm wide by 15 mm long. Roll the paper into a cylinder and place it about halfway into the hole in a 1x2 block, with the gap toward the top (the face with the two bumps on it). Place the front of the photodiode (with leads horizontal as in the case of the LEDs) into the center of the paper cylinder and press firmly into the block.



Basic Transmission Assembly:

 For convenience we will mount the entire assembly on the breadboard, with the photodiode and LED plugged directly into the socket strip. This means that the overall area should be small and that the height of the photodiode and LED should allow them to be securely plugged into the socket strip. To meet the first criterion, we will use a 2x4 plate as the base.
To adjust the vertical position of the photodiode and LED we will use 1x2 plates. Place two of these at each end of the base plate.
Bend the leads of the photodiode and LED downward and twist each pair by 45°. Position the assembly in the center of the lower socket strip of the breadboard, with the LED on the left, and carefully plug in the leads (remember that each lead must plug into a separate column).
We now have an optical path, of length approximately equal to three times the basic Lego pitch, with an LED at one end and a photodiode at the other. This will be our basic apparatus for transmission measurements.

Part 2: Photodiode Amplifier

The inverting op-amp circuit works by taking the current that flows into the "virtual ground" at the inverting input and forcing it to flow in the feedback resistor. Since the voltage across $R_F$ is equal to $R_F I_F$ , the output voltage (on the other terminal of $R_F$ ) is proportional to the current flowing into the virtual ground. What if instead of this current originating from the voltage across $R_1$ , it instead came directly from a current source? Well, the output voltage would still be proportional to it: $v_{out} = -R_F I_F = -R_F I_{in}$ I.e. we have an amplifier which accepts a current as an input and produces a voltage as an output. This is called a transresistance amplifier. (Since a resistance converts its current to a voltage ($v=Ri$ ), a transresistance converts a current in one part of the circuit to a voltage in another.)
\includegraphics[scale=0.500000]{photo_opamp.ps}
Fig. 5.5: Photodiode Amplifier


Construction:

 Wire the circuit in Fig. 5.5 to the left of the emitter-detector pair near the photodiode. Leave enough space to the right of this circuit for an additional op-amp.

Testing:

 Turn on the under-shelf florescent lamp and monitor $v_{out}$ with the oscilloscope. You should see a DC value with a significant amount of 120 Hz ripple.

Observations:

 Get one of the remote control transmitters from the cart. Aim it at the photodiode from a reasonable distance, press a button, and observe the resulting output waveform. Return the transmitter to the cart as soon as you finish this step, as we don't have very many.

Question 1:

 Analyze the transresistance amplifier using the op-amp design rules and convince yourself (and the grader) that $v_{out}$ really does equal $-R_F i_d$ .

Part 3: LED Driver

If we drive the LED directly from the function generator (as we did in Part 4 of Experiment 2.4) the resulting optical signal is badly distorted since the LED only conducts on the positive half-cycle of the waveform. We can fix this problem by using the OFFSET control to add a DC bias to the signal. If the bias is greater than the amplitude of the AC component, the signal is always positive and the LED will always conduct. However, there is still some distortion due to the exponential i-v relationship of the diode. Since the brightness of the LED is proportional to current and our signal sources put out voltages, we need a voltage-in, current-out or transconductance amplifier.

The simplest way to get a transconductance amplifier out of our basic inverting amplifier configuration is to replace the feedback resistor with the element whose current we wish to control, in this case the LED:

\includegraphics[scale=0.500000]{ckt6.1.5.ps}

To get the offset we need to avoid clipping, we can add a second input and connect it to one of the power supplies. In this case, to forward bias the diode, we must connect it to the negative (-15 V) supply.

\includegraphics[scale=0.500000]{ckt6.1.6.ps}

One more enhancement and we're done. We would like to be able to monitor the current in the LED. To do this we simply add a current sensing resistor in series.

Putting this all together we get the following:

\includegraphics[scale=0.500000]{ckt5.3.5.ps}
Fig. 5.6: LED Driver


Construction:

 Wire the circuit as shown above directly to the left of the LED in the emitter-detector pair.

Testing:

 Set the function generator to produce a 1 V p-p, 1 Hz square wave and connect it to $v_{drive}$ . The LED should get brighter and dimmer, but never be completely extinguished.

Observations:

 Connect a 1 v p-p, 1 kHz triangle wave to $v_{drive}$ . Observe the resulting $v_1$ and $v_{LED}$ . Point the LED at the photodiode and observe the output of the photodiode amplifier. Do we finally have satisfactory linearity of the LED/Photodiode system?

While observing both $v_1$ and the photodiode amplifier output on the oscilloscope, determine the maximum value $v_{drive}$ can have before distortion occurs.

Question 2:

 Analyze the above circuit and determine the relationship between $v_{drive}$ and $i_{LED}$ . What is the quiesecnt current (i.e. with no input signal) in the LED? Assuming $v_{drive}$ is a standard 1 V p-p signal, what are the minimum and maximum peak current values?

Part 4: More Gain for the Photodiode

With nothing but air between the LED and the photodiode, our photodiode amplifier gives a satisfactory output. However if we want to be able to measure objects with high optical density, we will need more sensitivity. Since the output voltage is determined by the product of the photodiode current and $R_F$ , we can get more output for the same input simply by increasing $R_F$ . Since the largest value resistor in our parts kit is 10 MΩ, we can increase the gain by a factor of 100, which should be enough.

However, there are a couple of reasons not to do it that way. One is that putting too much gain in a single stage can lead to problems, including reduced bandwidth. Another is that this would amplify the DC component of the signal (due to ambient light) by the same amount as our (much smaller) LED signal. This could cause the amplifier to saturate (clip), causing complete loss of the desired signal. Adding a second stage, with a DC blocking capacitor between the stages, eliminates both of these objections.

\includegraphics[scale=0.500000]{ckt5.3.6.ps}
Fig. 5.7: Improved Photodiode Amplifier


Construction:

 Add additional components to your existing photodiode amplifier to produce the circuit above. The addidional circuitry should be placed directly to the right of the original photodiode amplifier that you built in Part 2.

Testing:

 Observe $v_{photo2}$ with the oscilloscope. You should see the 120 Hz ripple due to the ambient flourescent lighting. With the 'scope set to DC, there should be no significant offset voltage.

Question 3:

 Ignoring the effect of the capacitor, what is the total transresistance gain ( $v_{photo2}/i_d$ ) for this circuit?

The Future:

 Don't disassemble the photodiode amplifier or LED driver circuits. We will be using them in future labs.