Chemistry 628 – Spring 2009 University of Wisconsin-Madison Lab Unit 2: Signal Amplification Using Op-Amps Many common transducers of analytical signals produce signals that are very small, either as voltages or as currents. For example, a typical photomultiplier tube in a spectrometer will produce a current on the order of picoamps to nanoamps. One of the most important steps in many analytical measurements is to amplify the signal. The difficulty in accomplishing this is that one needs to amplify the signals without also amplifying the noise. Operational amplifiers, or "op-amps", are the most practical way of amplifying signals for the vast majority of all analytical measurements. In this lab you will look at some of the basic op-amp circuits and investigate their performance. You will also look at some properties that can limit their performance, such as frequency response (or speed) and noise. I. Inverting Amplifier -+opampR1R2VinVoutV--V++The inverting amplifier is one of the most common amplifier circuits and is shown above. For an ideal op-amp with infinity gain, we can usually make two approximations that greatly simplify the design of op amp circuits. The first approximation is that the op amp does whatever it can do to make the voltages at the inverting ( ) and non-inverting (v) inputs the same. That is, the op amp tries to make−v+−+=vv. The second approximation is that the inputs of the op amp draw no current. Using Kirchoff's current law and the assumption that no current flows into the op amp gives: 2Rvv1Rvvoutin−−−=−. Recognizing that (from the first assumption above) gives the gain equation for an inverting amplifier: 0==+−vvRev. 2/1/20091R2Rvvinout−=. In the following exercises, you will look at both the frequency response and the noise of the inverting amplifier. A. Bandwidth and Gain 1. Measure the Bandwidth Construct the inverting amplifier circuit (shown on the previous page) using an OP27 operational amplifier. Use R1 = 100 ohms and R2 = 100,000 ohms (100 kilohms, or more commonly, “100 k”). Set the function generator to produce a small sine wave of approximately 10 millivolts peak-to-peak at a frequency of 100 Hz. Look at both the input and output signals on the oscilloscope. What are the peak-to-peak input and output voltages? Is there a phase shift? Keeping the input voltage fixed, look at the signal output as a function of frequency of the input signal. You should see the output signal start to decrease in amplitude at high frequencies. Try to identify the “3 dB point”, where the output voltage decreases by 2/1and the phase shift changes by another 45 degrees. Record the amplitude and phase at enough different frequencies that you will later be able to make a plot of gain vs. frequency and phase vs. frequency. Keep in mind that you do not need many data points in regions where no change is occurring. More data points are needed in regions of rapid change. Note that the "bandwidth" of the op amp circuit is the range of frequencies that the circuit amplifies. The low frequency end of the "band" is essentially 0 Hz, since the circuit has no trouble amplifying DC signals. The high frequency end of the "band" is the cut-off frequency. At frequencies higher than the cut-off, the gain begins to drop off. So by measuring the cut-off frequency, you are essentially measuring the bandwidth. 2. Change the Gain and Measure the Bandwidth Change the gain of the circuit by replacing resistor R1 with a larger resistor of 1,000 ohms (1 kilohms, or simply “1 k”). Again, look at the magnitude at low frequencies. Determine the bandwidth of this circuit. In this case, you do not need to make complete measurements for a Bode plot. Instead, you can quickly find the cut-off frequency (the 3 dB point) by looking at the output for a voltage drop of 2/1 and a 45 degree additional phase shift. Then check the output voltage and phase at one or two frequencies above and below the cut-off to confirm that your measurement makes sense. At what frequency does the roll-off in response occur? Rev. 2/1/2009 23. Change the Gain Once More Replace resistor R1 with an even larger resistor of 10,000 ohms (10 kilohms, or simply “10k”). Again, look at the magnitude at low frequencies and then determine the bandwidth. At what frequency does the roll-off in response occur? 4. And Again Replace resistor R1 with an even larger resistor of 100,000 ohms (100 kilohms, or simply “100k”). Note that this is a unity gain amplifier. Find the frequency where the roll-off in response occurs. You may see some interesting behavior called gain peaking at the frequencies just before the gain starts to drop. If you do, be sure to record this. In steps 1 through 3 above you hopefully saw that the “bandwidth” (the range of frequencies capable of being amplified) depends on the gain of the amplifier. So, you can’t make a single amplifier that is both high gain and high speed, for example. To do that you’ll need to cascade multiple amplifiers together to make a multi-stage amplifier. B. Noise 1. Intrinsic Noise and Noise Pick-up Go Back to first amplifier configuration in Part A (the highest-gain configuration, with R1 = 100 ohms and R2 = 100,000 ohms). Instead of connecting to the function generator, connect the input wire (on the left side of R1) directly to the non-inverting input using the shortest wire possible. At this point, you have the input defined as zero volts. For a perfect amplifier, the output would be exactly zero. Now you are going to look at the noise. Connect the output of the circuit to the oscilloscope and set the scope to trigger on "line". There are often 2 sources of noise: one is the intrinsic noise of the electronics, which is usually distributed over a wide range of frequencies. The second source of noise is “pickup”, which often comes from the magnetic fields associated with anything that uses 110 VAC as its energy source. By triggering on "line", anything that is synchronized with the 110 VAC power line will be stationary on your scope. Anything that is fluctuating is at some other frequency. Chances are you will see both stationary 60 Hz noise and plus fluctuating "fuzz" noise. The stationary waves are at 60 Hz, 120 Hz, 180 Hz, and other multiplies of the 60 Hz power line. The "fuzz" noise comes from the other environmental sources and the intrinsic noise of the circuit. Rev. 2/1/2009 3Measure the