Week 7 PDF: Biopotential Amplifiers

Part I Basics  A differential amplifier (diff amp) is an electronic amplifier in which the output voltage is proportional to the difference between two input voltages. Diff amps are useful for measuring biopotentials, since many biopotentials consist of the difference in voltage on two bo...

Part I Basics  A differential amplifier (diff amp) is an electronic amplifier in which the output voltage is proportional to the difference between two input voltages. Diff amps are useful for measuring biopotentials, since many biopotentials consist of the difference in voltage on two body sites. The ECG, for example, is measured as the difference in surface potential between two limbs. The electroencephalogram (EEG) is the difference in surface potential on two skull sites. Likewise, the electromyogram (EMG) records the difference between two potentials measured on a muscle. The diff amp is ideal for measuring these difference potentials and is thus often used in medical instrumentation. The mathematical definition of the diff amp is: where V1 and V2 are input voltage VOUT is the output voltage Ad is the differential voltage gain. A property of the diff amp is that it tends to eliminate common-mode voltage interference. Common-mode voltages are those that have the same value on all input terminals. This means that if V1 and V2 are common-mode voltages, then V1 = V2, and the output VOUT is zero. That is, the output voltage due to common-mode interference tends toward zero in a diff amp. This fact helps reduce interference in biopotential amplifiers. 1. A Transistor Differential Amplifier The transistors are assumed to have a small emitter resistance re such that βre ≪ rb and it can be neglected. The a.c. equivalent circuit for the differential amplifier is formed by replacing the bias supply with a short circuit, and by replacing the transistors Q1 and Q2 with their a.c. equivalent circuit. The following figure is used to compute the output voltage, VOUT. The differential gain of the diff amp is: Inverting and Noninverting Amplifiers: The differential amplifier can be connected in either the inverting or noninverting mode. The inverting mode is achieved by shorting the source VS2 to ground (VS2 = 0). The -ve sign indicates that the o/p voltage is 180𝑜 out of phase with the i/p. (i.e., the o/p voltage is inverted in phase). The gain (AI ) is: the gain is negative. A diff amp in an inverter connection. On the other hand, if the source number 1 is shorted to ground (VS1 = 0), the output VOUT becomes The gain (ANI ) is: The +ve gain means that the o/p voltage is in phase with the i/p voltage, and the amplifier operates in its noninverting mode. 2. Operational Amplifier Analysis Amplifiers that use ideal differential amplifier chips as components, along with other R, L, and C components, are called operational amplifiers (op amps). The term "operational" is used because these circuits perform mathematical operations (multiplication or integration) on the input voltage. The voltage gain of the circuit is: An op amp loaded with impedance ZL High-Input-Impedance Amplifiers with Controlled Gain: As a rule, the higher the input impedance of an amplifier, the better. The basic reason for this is that when the input impedance is high, it will draw very little current from previous transducers or amplifiers. This means it will not disturb the voltages and the currents of those devices, and is in a sense “invisible” to them. If the amplifier had a lower impedance, it would draw more current from the source, altering the signal and potentially distorting the measurement. A high input impedance helps to avoid this problem, making the amplifier more "invisible" to the source, so the original signal remains intact. On the other hand, the input impedance of practical amplifiers is lower than this. To avoid the distorting effects of amplifier loading on the body potential source, it is necessary to use a high-input-impedance buffer. The simplest buffer using op amps: A buffer circuit In this circuit the input impedance ideally would be infinite. V1 at node 1 equals VIN and is tied directly to VOUT. This amplifier preserves the high input impedance of the ideal diff amp while reducing its gain to the value of one. An amplifier that gives more control over the gain while preserving the high input impedance is shown: A noninverting amplifier The gain of this amplifier therefore be controlled by Rf and Ri Differential Amplifier with Controlled Gain: The previous amplifier (noninverting amplifier) is not a differential amplifier, because it does not satisfy In order to make it a diff amp, we add a potentiometer (RP) and adjust it so that the circuit is balanced.  This is a diff amp when Equation is satisfied. The potentiometer (RP) is added. The resistance below the wiper arm is α 𝑅𝑝 , and the resistance above the wiper arm is (1 − α) 𝑅𝑝. This is true because the sum of these comes to RP  (unbalanced circuit) (balanced circuit) The differential gain is: Buffer Amplifier for a Diff Amp: In order to buffer both leads of a diff amp, such as given in the left figure, and to provide amplification at the same time, the right circuit is used. A buffer circuit for a diff amp. The gain of this amplifier is: 3. Biopotential Measurement Interference The importance of diff amps is heightened by the fact that one of the major tasks in monitoring, diagnosing, and making measurements on patients is the measurement of potential differences that occur in the body, such as the ECG, EOG, EEG, and EMG. They are all measured as differences between sites on the surface of the body. In each case the instrument for doing this is the diff amp. The situation in making a difference measurement on the body is shown in the following figure. Power-line interference in biopotential measurements This illustrates a basic problem of such a measurements in the hospital environment: power-line, 60-cycle (~) interference. In such an environment, where thousands of pieces of electrical equipment are in use, the power requirements are high. Inevitably, patients are in close proximity to power buses and are therefore capacitively coupled to the power buses through the stray capacity between them and their bodies, which are essentially conductors. The amount of capacity can be estimated from: where A is area in square meters d is the distance between the plates in meters Stray capacity values between 1 and 10 pF to couple a patient to the power lines. If the voltage V2 equals V1. Therefore these are called common-mode voltages. The output voltage would be the difference This is one reason diff amps are used in this application. That is, the output of the diff amp due to the common-mode voltage interference is approximately zero. This, in the ideal case, eliminates that interference. Common-Mode Rejection in a Diff Amp: The power-line interference may exceed the level of the signal being measured. This is cancelled by the fact that the interfacing signal appears equally intense at both input terminals of the diff amp, and is therefore called a common-mode signal. In this case the resulting output voltage is proportional to the difference of two equal voltages, which is zero. Since one of the functions of the diff amp is to reject the common-mode signal. The common-mode rejection ratio (CMRR ) measures how well the rejection occurs. The CMRR is a voltage ratio A diff amp