Biomedical Electronics Bioinstrumentation Review on Electrical Laws Contents
Biomedical Electronics & Bioinstrumentation Review on Electrical Laws
Contents Ohm’s Law Kirchhoff’s Voltage & Current Law Voltage & Current Divider Rule Series & Parallel Resistive Circuits Capacitance
Voltage & Current Voltage is the energy required to move a charge, q between two locations in an electric field. WAB ∆V = q Where, V : Voltage W : Work q : Charge How much work is required to move an electron from 0 V to 4 V? (q = 1. 6 x 10 -19 C)
Voltage & Current is the flow rate of electrons per second. d. Q I = dt Where, I : Current Q : Charge t : Time
Resistance l I Vb Resistance V Va of a conductor is given by: l R= a Where, R : Resistance : Resistivity l : Length a : Cross-section
Series Resistors For any number, n of resistors, RT = R 1 + R 2 + … + Example: Rn R 1 R 2 R 3 V RT = R 1 + R 2
Parallel Resistors For any number, n of resistors, Example: V 1 =1+ 1+…+ 1 RT R 1 R 2 Rn R 1 R 2 R 1 R 2 RT = R 1 + R 2
Series & Parallel Combination Find the total resistances, RT for the following circuits: R 2 R 1 R 3 V R 2 (a) R 4 R 3 V R 4 (b)
Ohm’s Law is given by the following formula: V = IR Where, V : Voltage I : Current R : Resistance The law states that the current is proportional to the applied voltage and inversely proportional to the resistance.
Ohm’s Law The following graph represents the relationship between the voltage, current and resistance. Voltage, V Resistance, R =∆ V ∆I Current , I
Power Represents the amount of energy dissipated by a component. P = IV Where, P : Power I : Current V : Voltage Derive the following expression for power. P = I 2 R
Kirchhoff’s Voltage Law (KVL) KVL states that the sum of voltage drops around the loop is zero. ∑V = 0 Starting from any point on the closed loop, all the voltage sources and voltage drops across each element can be added. V 1 V 2 VS VS = V 1 + V 2 I
Voltage Divider Rule Permits determination of the voltage across a series resistor without knowing the current of the circuit. RA RA V VA = RA + R B V RB RB V VB = RA + R B
Kirchhoff’s Current Law (KCL) KCL states that the current entering or leaving any nodes are zero. ∑I = 0 This means that the current entering a node must equal to the current leaving the nodes. I 3 I 1 I 3 = I 1 + I 2
Kirchhoff’s Current Law (KCL) The following demonstrates single branch current entering a node splits out to two current branches. I 3 I 1 I 2 I 3 = I 1 + I 2
Current Divider Rule Current through any branch of a parallel resistive network is equal to the total resistance of the parallel network divided by the resistor of interest and multiplied by the total current entering the parallel configuration. RT 1 T Ix = Rx
Current Divider Rule Derive the following expressions. R 1 RS R 2 V R 21 T I 1 = R 1 + R 2 R 11 T I 2 = R 1 + R 2
Wheatstone Bridge Observe the following circuit: RS R 1 V R 2 Va Vb R 3 R 4 To get a balanced bridge where Vb Va is zero, R 1 = R 3 R 2 R 4
Capacitance is the measure of a capacitor’s ability to store charge on its plates. Q C= V Where, C : Capacitance Q : Charge V : Voltage
Capacitance The relationship between capacitance, current and voltage are given as follows. d. V I=C dt Where, I : Current C : Capacitance V : Voltage t : Time
Series Capacitors For any number, n of capacitors, 1 =1+ 1+…+ 1 CT C 1 C 2 Cn Example: C 1 V C 2 C 1 C 2 CT = C 1 + C 2
Parallel Capacitors For any number, n of capacitors, CT = C 1 + C 2 + … + C n Example: V C 1 C 2 C 3 CT = C 1 + C 2
Capacitor’s Physical Dimensions With regards to the physical dimensions, capacitance can be represented as: �� A C= d Where, C : Capacitance �� : Permittivity A : Area d : Distance between plates
Further Reading… 1. Boylestad, R. L. (2007). Introductory Circuit Analysis. 11 th Ed. , Prentice Hall. ü Chapters 1 -7 & 10
Biomedical Electronics & Bioinstrumentation Review on Operational Amplifier
Contents Principles of Operational Amplifier Ideal vs Practical Op-Amp Inverting & Non-inverting Configuration Basic Application of Operational Amplifiers
Operational Amplifiers Early operational amplifiers are used for the following purposes: i. iii. iv. Addition Subtraction Integration Differentiation Consists of two terminals. Operate with two dc supply voltages.
Ideal Versus Practical Ideal characteristics are used to understand simplify the analyses. Practically impossible to achieve these standards. Characteristics Ideal Practical Voltage Gain ∞ Very high Bandwidth ∞ Very high Input Impedance ∞ Very high Output Impedance 0 Very low
The Ideal Op-Amp Av = ∞ Vin Zin = ∞ + Av. Vin Zout = 0 Vout
The Practical Op-Amp - Vin Zin + Av. Vin Zout Vout
Internal Block Diagram Differential amplifier input stage Voltage amplifier gain stage Push-pull amplifier output stage
Op-Amp Parameters Common-Mode Rejection Ratio (CMRR) Common-Mode Input Voltage Range Input Offset Voltage Drift with Temperature Input Bias Current Input Impedance Input Offset Current Output Impedance Slew Rate Frequency Response
Negative Feedback Used to stabilize gain and increase frequency response. The extremely high open-loop gain creates unstable situation. Open-loop gain parameter varies greatly between devices. Negative feedback use portion of output and applies out of phase with the input.
Non-Inverting Configuration Signal applied to positive input. Output applied back to inverting input through feedback circuit. Vin + - Vout Rf Ri Ani = 1 + Rf Ri
Inverting Configuration Signal applied to through a series resistor Ri to the inverting input. Output is fed back through Rf to the same input. Positive input grounded. Rf Vin Ri + Vout Ai = - R f Ri
Voltage Follower Special case of non-inverting amplifier. All of the output voltage is fed back to the inverting input. Closed-loop gain is 1. Vin + - Vout
General Application Comparators ◦ Zero level detector ◦ Non-zero level detector Summing Amplifiers Integrators Differentiators
Further Reading… 1. Floyd, T. L. (2008). Electronic Devices. 8 th Ed. , Prentice Hall. ü Chapter 12 & 13
- Slides: 38