in this paper comparison is made on the basis of soil strata. Various responses are taken for the comparison. STAAD PRO software is used for analysis. PEB structure is used for analysis in staad pro software. Prof. G. S. Patil | Dr. Prof. M. B. Choug
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INTRODUCTION
Introduction
The purpose of this assignment is to design a precise circuit (ohmmeter) that can measure resistances ranging from 0.01Ω to 10kΩ to high accuracy of 0.1%. Sometimes while measuring resistances using ohmmeter, it will display useless reading even if the resistance is not measured using it. For e.g. the ohmmeter will display 0.18Ω - 0.2Ω though the resistance is lot less than that. This error displayed by ohmmeter mainly due to: a) Resistance of ohmmeter cables are measured. Though wire resistance is very small, the length of the ohmmeter cables that are long enough and if very small resistance is required to be measured, it will introduce the measurement error as the ohmmeter measures the resistance of the cables in circulating loop as shown in gure 1.
Figure 1: Interpretation of wire resistances and resistance of the device to be measure b) Sometimes ohmmeters are not designed to be precise enough to measure very small resistance. c) The contact resistance of the test probes. There are several solutions that can be done in order to minimize these problems. One of the technique that is simple and eective technique known as Kelvin (4 wire) Resistance measurement. Consider simple circuit shown in gure 2.
Figure 2: Simple Kelvin Resistance measurement example No matter what current will ow through the resistor, the current will always be 1A as it is supplied by a constant current source. By ohms law, 1
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DESIGN OF THE CIRCUIT
V = IR
(1)
V I
(2)
∴R=
Since I = 1 A, V = R. For e.g. if 10mV is measured across the tested wire, it means resistance of the wire is 10mΩ . Since the current is same throughout the circular loop, the contact resistances of the alligator clip and wires are no more a problem. Hence the measurement of voltage across the device under test gives value of resistance directly without any further computation. The input impedance of the voltmeter is very high (in Mohms), almost no current ows into the ohmmeter therefore it does not eect the circuit. Therefore the contact resistance of the test probe which is likely to eect the resistance measurement is eliminated. Measurement accuracy may be improved even further if the voltmeter's current is kept to a minimum, either by using a high-quality (low full-scale current) movement and/or a potentiometric (null-balance) system. By applying the principle of Kelvin resistance measurement technique, precise circuit that can measure resistance with high accuracy will be designed and simulated in SPICE software.
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Design of the circuit Description of the circuit
The circuit arrangement shown in gure 3, used in order to cover the resistance range as per the required accuracy that eliminates the error caused by the contact resistance.
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2.1
Description of the circuit
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Figure 3: Schematic of the circuitry 3
DESIGN OF THE CIRCUIT
2.1
Description of the circuit
2
DESIGN OF THE CIRCUIT
To understand this design properly, the circuitry is split into 3 parts: 1. Constant current source: Since sinusoidal test signal is to be applied, simple transconductance amplier i.e. the oating constant current source has been used instead of signal controlled referenced current source shown in gure. As the ac current ow through the transistors of the referenced current source, it causes disintegration of them eventually the transistors to malfunction. When the signal is negetive at the base of NPN transistor, it indicates that the base-emitter diode is reverse-biased. The ampli er stops working as the diode acts like an open circuit. As the negetive signal becomes too high, the base-emitter diode will blow up. The same principal even applies to the PNP transistor. Hence oating current source for the resistance Rx that is to be measured is used. 2. Input Stage: It comprises of two operational ampli ers in conjunction with adjustable gain with resistor Rg . It provides very high input impedance on both inverting and non-inverting terminals of the dierential ampli er since the input impedances of it have nite value i.e. R1 and (R3 + R4 ). The inverting and noninverting terminals of the instrument ampli er are connected across the resistor Rx such that the potential dierence is developed across it. 3.Output stage: It is basically a dierential ampli er. All 4 of the resistors R1 , R2 , R3 and R4 are matched accurately around the op amp in order to reject common mode voltage and noise. The voltage across the resistor Rx is ampli ed at this stage to give an output voltage Vout and it is referred to the output ground. Setting up a value for constant current source: Assume test sinusoidal signal of amplitude 1 V is applied. Maximum voltage output of the circuit is also required to be 1V. Since the resistances ranges from 0.01 to 10k is to be measured, choose input resistance Rin of the voltage to current converter to 10k i.e. Rin = 10k. Equation for the current source is derived followed by computation of supply current IS : By golden rule: V+−V− =0
∴V+ =V−
∴ IS =
VS Rin
VS = 1V and Rin = 10kΩ ∴ IS =
1 = 0.0001A 10 × 103
Hence constant supply current IS is 0.0001A or 0.1mA. Matching the resistor values of the instrumentation ampli er: The resistances for the instrumentation amp is given by R1 = R3 , R2 = R4 and R5 = R6 .
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(3)
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SIMULATION AND ERROR ANALYSIS
The dierential gain is given by: Ad =
2R5 R2 × (1 + ) R1 Rg
(4)
Voltage input and voltage output are required to be equal. Hence unity gain is required from the instrumentation amplifer. Therefore following parameters from equation 4 are equalized: Take the ratios
R2 R1
=
1 2
and
2R5 Rg
=
2×1 2
∴ R1 = 2 × R2 and Rg = 2 × R5
Substituting the parameters above in equation 4 to give dierential gain Ad : 1
1 2 × 1 Ad = × (1 + 1 ) 2 2 ∴ Ad =
1 × 2 = 1 2
Hence R1 = 2R2 and Rg = 2R5 . Operational ampli er LTC1052 is chosen over UA741. In the table 1, it is reasoned out why LTC1052 model is used: Table 1: LTC1052 vs UA741 LTC1052 Slew rate: 0.5V /µs Maximum oset voltage: 15mV Minimum CMRR: 70dB Maximum input bias current: 30pA
UA741 Slew rate: 4V /µs Maximum oset voltage: 5µV Minimum CMRR: 120dB Maximum input bias current: 1500nA
Many other features of LTC1052 can be found that excels UA741 features by referring to the datasheet. At later stage, the AC output will be converted into DC such that it is interfaced with Analogue to Digital converter.
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Simulation and error Analysis
Initially there was oset voltage value for resistance 0.01.
