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King Abdulaziz University Faculty of Engineering Department of Electrical and Computer Engineering EE306 – Electrical Engineering Technologies 2ND LAB SESSION: LOADING EFFECT IN ELECTRICAL MEASUREMENTS Objective Appreciating measurement errors resulting from loading effect while testing electric potential of circuits with high output impedance relative to the input impedance of the measuring device. Background Suppose we want to measure the output voltage (𝑉𝑜 ) of the circuit shown in Fig.1 using Oscilloscope through a 1x probe. Theoretically speaking, if the input voltage to the circuit from the function generator is 1 Volt peak-to-peak (𝑉𝑝𝑝) at 100Hz, the output voltage (𝑉𝑜 ) of this circuit without the oscilloscope being attached can be calculated as follows: 𝑉𝑜 = 𝑅2 𝑅1 +𝑅2 × 1𝑉𝑝𝑝 Eq.1 Figure 1 Voltage Divider circuit while connected to Oscilloscope through 1x probe [1] However, once the oscilloscope is attached through a 1x probe (which is a coaxial cable made of two conducting materials, one is the core made of a copper rod for connecting the signal to be probed, and the other is the shell made of a network of fine wire strips for connecting the ground and shielding the signal against electromagnetic interference), the output voltage would instantly change to the following: 𝑅2 //𝑅𝑖𝑛 1 +𝑅2 //𝑅𝑖𝑛 𝑉𝑜 ′ = 𝑅 EE306 × 1𝑉𝑝𝑝 Eq.2 Loading Effect The measurement Absolute Error (∆𝑉𝑜 ) can be calculated as follows: ∆𝑉𝑜 = 𝑉𝑜′ − 𝑉𝑜 Eq.3 If any Correction (𝑘) to be added to the measured voltage, it should equal to: 𝑘 = −∆𝑉𝑜 Eq.4 The Relative Error (𝑝) can be calculated as follows: 𝑝% = ∆𝑉𝑜 𝑉𝑜 × 100% Eq.5 This is a type of Systematic Errors happens due to what is called Loading Effects, which can be reduced by using 10x probe that makes the input impedance of the oscilloscope equals to 10MΩ instead of 1MΩ, see Fig.2. Accuracy (α) of the measurement can be calculated as follows: 𝛼 = 100% − 𝑝% Eq.6 For even higher accuracy, sometime 100x probe is needed, which has 100MΩ input impedance. Figure 2 The equivalent circuit of the oscilloscope when connected through a 10x probe [2] Preliminary Work 1) Use Eq.1 calculate the theoretical value (agreed true value) of the output voltage. 2) Use Eq.2 to calculate what is expected to be measured after taking into account the loading effects of the oscilloscope input impedance. 3) Use Eq.3 through Eq.6 to analyze the expected measurement error and accuracy. EE306 Loading Effect Experimental Procedure 1) Get a sine wave of 1 V peak-to-peak and 100 Hz frequency from the function generator. This should be the input signal to the circuit shown in Fig.1. 2) Use a breadboard and two 100kΩ resistors to connect the circuit shown in Fig.1. 3) Use 1x probe to connect the output of the circuit to the oscilloscope. 4) Adjust the vertical control of oscilloscope to have one of the output signal peaks right on one of the vertical divisions on the oscilloscope screen. 5) Count how many number of division and sub-divisions between the minimum and maximum peaks, multiply (No. of divisions + 0.2 × No. of sub-divisions) by the “Volts/Div” selected and/or shown on the screen to get the peak-to-peak voltage. 6) Connect 10x probe and repeat step 5. In Your Report 1) Use Eq.1 through Eq.6 to fill the following table for both the 1x probe and 10x probe experimental data. Data Set VO (Vpp) VO’ (Vpp) ΔVO (Vpp) k (Vpp) p (%) α (%) 1x (Expected) 1x (Measured) 10x (Expected) 10x (Measured) 2) What type of error resulting from this loading effect? Is it Grave, Systematic, or Random? Why? 3) Discuss with the lab engineer what could be the reasons behind the discrepancies between the expected the measured values. 4) Comment on that based on you understanding. References (other than the main course textbook) [1] http://www.digikey.com/schemeit/, Digikey Corp., visited on 23rd of June 2015. [2] http://mechatronics.mech.northwestern.edu/design_ref/tools/oscilloscopes_01_probes.ht ml, Northwestern University, visited on 23rd of June 2015, created on 12th of August 1999. EE306 Loading Effect