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MSU PHY 252 - amplifier

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1 THE AMPLIFIER OBJECTIVES: 1) Explain the operation of the differential amplifier. 2) Determine the gain of each side of the differential amplifier. 3) Determine the gain of the differential amplifier as a function of frequency. 4) Determine the common mode rejection percentage of the differential amplifier. INTRODUCTION In this experiment it will be our goal to acquaint you with the differential amplifier and how the device can be used to measure small bio-electric signals. Before using the device as a tool in biological and physiological measurements, it will benefit you to have some idea of the basic structure of the differential “amp”. The differential amp is basically a device that takes the "difference" between two voltage signals. The result of this subtraction is then amplified (or increased) so that it can be conveniently viewed on an oscilloscope or other recording devices. We will see the usefulness of subtracting two voltage signals in next week's experiment when we use the differential amp to view cardiac signals and muscle potentials. A schematic diagram of a differential amp is shown in figure 1. A-B = C subtractorkamplifier kCOUTPUT(Red)(Red)(Black)ABA-BINPUTS Va Vb Vr Figure 1 In the above diagram, the first red input lead has voltage Va, the second has Vb, and the black lead defines a reference voltage Vr. The input signals can be thought of as the voltage differences between the input lead and the reference voltage: A = Va - Vr B = Vb - Vr The subtractor part of the differential amplifier forms the difference between the two input leads: C = A - B = Va - Vb. The voltages here refer to voltages at any particular instant of time.Introductory Physics Experiments (Physics 252, v4.0) 2 This signal (A - B) is then sent through an amplifier and its amplitude gets increased "k" times. The signal k×(A-B) becomes the output from the differential amp. The value "k" is the GAIN of the amp. GAIN = outputinput The amplifier part of the differential amplifier makes voltages bigger at each moment. It cannot make the input voltage vary more or less quickly. Thus, an ideal amplifier has no effect on the frequency of its input signal C = A - B or on the shape as a function of time. It only changes its size. Of course, the signal A - B can be quite different from A or B by themselves. It might appear as if the differential amplifier takes the hard way by amplifying (Va - Vr ) - (Vb - Vr ) instead of amplifying (Va - Vb ) directly. Any real amplifier actually produces (as you will measure) an output related to not just the difference of its inputs, but also to their sum. So without the reference signal, we would have: Output = k × (Va - Vb ) + g ×Va+Vb2    where g is known as the “common mode” gain, the gain for an input presented in “common” to both inputs of the amplifier: if Va = Vb = Vcomm , Vcomm = (Va + Vb ) / 2 . An ideal differential amplifier would amplify only the difference, with g = 0 and k=100 or so. How close it comes to this is measured by the common mode rejection ratio, CMRR = (1 – g / k ) × 100% Stray electrical signals from outside sources, called noise, pervades the room where voltages Va and Vb are measured. The amplitude of this noise is often much greater than the amplitude of the biological signals to be studied. Since this noise is common to any signals measured in the same area, we can make a third measurement, Vr, of just the noise: Va = A + noise Vb = B + noise Vr = noise Without using the reference signal, the noise cancels in the difference term, but not in the sum term. Our imperfect amplifier would produce: Output = k × (A - B) + g × A + B2+ noise    The differential arrangement uses as inputs A = (Va+ noise) – (Vr+ noise) and B = (Vb+ noise) – (Vr+ noise). Now, the noise also cancels in the sum term and we get: Output = k × (A - B) + g × A + B2   The Amplifier (Version 4.0, 8/23/2002) 3 Note if all inputs are equal, Va= Vb = Vr , then A = B = 0, and we expect zero output. Since the noise is much larger than the desired signals A and B, the arrangement which subtracts the reference voltage produces much less contamination of the output signal. The biological signals would be completely obscured if not for this property of the amplifier, which is known as Common-Mode Rejection, because it rejects signals sent in common to both of the input leads. We will measure the characteristics of the amplifier by arranging input signals of A=0, then B=0, and finally A=B. From the equations above, the output for these conditions should be Out(A=0) = -B(k - g/2) ≈ -kB if g << k Out(B=0) = A(k +g/2) ≈ kA if g << k Out(A=B) = Ag A second feature of the differential amplifier is that it can be "AC coupled". This means that there is an electronic circuit that passes only input potentials varying fairly rapidly in time. The AC coupling circuitry will not pass constant voltage DC or slowly varying voltage at frequencies below 1/2 cycle per second. AC coupling also removes any DC component from an AC signal. For example, a signal that varies from 5 mV to 15 mV at, say, 10 Hz, is an AC signal with a DC component of 10 mV. (See Figure 2.) The AC coupler will remove the 10mV DC component and pass an AC signal varying from -5 mV to +5 mV to the amplifiers. AC coupling is accomplished by capacitors in the input circuit that act as a large resistance to DC signals. The differential amplifier may also be "DC coupled" with no restriction on the input. It amplifies whatever it sees at the input: AC, AC + DC, or pure DC. Note that the oscilloscope may also be AC-coupled using the switch under the input connector. Before AC coupling 151050-5-10TimeVoltage (mV)DC - Component (10mV)Introductory Physics Experiments (Physics 252, v4.0) 4 After AC coupling: (DC component eliminated) 151050-5-10TimeVoltage (mV) Figure 2 In next week's experiment we will look at a specific biological measurement, the electrical potentials produced by the human cardiac muscles. The heart puts out a signal varying from about -4 mV to +4 mV at a frequency of about 72beats60sec = 1.2 Hz corresponding to the contractions of the cardiac muscles. Customarily, placing an electrode on the skin of each arm makes this measurement. There is an arm-to-arm DC potential of about 20 mV due to the biceps and shoulder


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