Latest Trends in Circuits, Control and Signal Processing A Rapid Inductance Estimation Technique By Frequency Manipulation LUM KIN YUN, TAN TIAN SWEE Medical Implant Technology Group, Materials and Manufacturing Research Alliance, Faculty of Biosciences and Medical Engineering, Universiti Teknologi Malaysia, Skudai 81310, Johor, Malaysia [email protected]; [email protected] Abstract:- Inductors or coils are one of the basic electronics elements. Measurement of the inductance values does play an important role in circuit designing and evaluation process. However, the inductance cannot be measured easily like resistor or capacitor. Thus, here would like to introduce an inductance estimation technique which can estimate the inductance value in a short time interval. No complex and expensive equipment are involved throughout the measurement. Instead, it just required the oscilloscope and function generator that is commonly available in most electronic laboratory. The governed theory and methods are being stated. The limitation of the method is being discussed alongside with the principles and computer simulation. From the experiment, the error in measurement is within 10%. This method does provide promising result given the series resistance of the inductor is small and being measured using proper frequency. Key-Words: -Inductor, Inductance measurement, phasor, series resistance, phase difference, impedance. • Current and voltage method which is based on the determination of impedance. 1 Introduction • Bridge and differential method which is based on the relativity of the voltages and There are many inductors being used in electronics currents between the measured and reference circuits. In order to evaluate the performance of impedances until a balancing state is electronic system, it is particular important in achieved. determining the inductance values as what happened • Resonance method which is based on to the resistance values. Especially for the system physical connection of an inductor with a which required the accurate operation of frequency capacitor to create a resonant system. like the tuning circuits and filters, the measurement of inductance value does play an important roles in For all that, these methods are not straight forward the designing process. and hard to be implemented except for the first one which is the current and voltage method. This is However, unlike the resistor or capacitor value which because some of them required complex calculation can easily be measured by using a typical multimeter, has to be involved before getting the result. the inductor value cannot be evaluated that way. Meanwhile, some of them required some circuit There are two methods generally used to determine configurations in order for the system to work[4]. the inductance value, which are using the theoretical These circuit configurations make the measurement formulae estimation as discussed in [1]and indirectly and contribute to the errors due to the experimental measurement. The theoretical tolerance of individual circuits elements[5]. As thus, estimation method only limited to certain commonly another simpler method based on the use of function inductors[2]. On the other hand,the inductance can be generator and oscilloscope is being utilized here as measured by using the LCR meter which is belong to an extension for the further expansion on the first the experimental measurement. However, the LCR method. Function generator and oscilloscope meter is not cheap to be purchased and normally not generally can be found in ordinary electronic equipped in the general working laboratory. The laboratory. It can be further utilized to perform this methods being used in measuring an inductance task without the present of any additional circuit falling into three categories[3]: components like resistors and capacitors. ISBN: 978-1-61804-173-9 13 Latest Trends in Circuits, Control and Signal Processing 2 Theory Assuming the series resistance of the resistor is negligible, impedance of an inductor is defined as 50 Ohm (4) ͒ Ɣ ͞!͆ According to the voltage divider rule Unknown Function Inductor Oscilloscope Generator ͐*0/ ͒ Ɣ ͐$) ͌ ƍ ͒ Fig. 1 Schematic for the configurations ͞!͆ Ɣ ͌ ƍ ͞!͆ For the passive elements R, L and C, we can ͦ ͦ represent the voltage and current in the phasor or ! ͆ ƍ ͞!͆͌ Ɣ ˄ ͦ ͦ ͦ ˄ frequency domain[6]. ͌ ƍ ! ͆ For a resistor, if the current through it is !͆ , the voltage across it is given ͝by Ɣ Ɣ ͦ ͦ ͦ ͌ ƍ ! ͆ Ohm’s̓(cosʚ!ͨ law ƍ as Ǧʛ TakingĢĨħ ͥ , so Ɣ (1) Ĝġ ͦ ͪ Ɣ ͌͝ Ɣ ͌̓(cos ʚ!ͨƍǦʛ For and inductor L, assuming the current through it 1 !͆ Ɣ ͦ ͦ ͦ is . The voltage across the 2 ͌ ƍ ! ͆ inductor ͝ Ɣ ̓ (iscosʚ!ͨ ƍ Ǧʛ Solving for L with ! Ɣ 2͚ $ (2) ͦ ͪ Ɣ ͆ / Ɣ Ǝ!͆̓(sinʚ!ͨ ƍ Ǧʛ ͌ ͆ Ɣ ǰ ͦ We can rewrite the equation as 32͚ʛ R=50, then (3) ͪ Ɣ !͆̓(cosʚ!ͨ ƍ Ǧ ƍ 90°ʛ By concluding both equation (1) and (3) and draw it ͨ.ͩͭͨͨ (5) ͆ Ɩ in phasor diagram as we can see it in Fig. 1. Ic is the ! current throughout the entire circuit, VLis the 3Equipmentand Method potential drop in inductor which is leading Ic by a phase of_and VR is the resistor’s voltage which is in 3.1 Equipment phase withͦ the current. Equipment which are being used in this experiment are the following: • Tektronix TDS 3014B Oscilloscope • Instek GFG-8210 Function Generator 3.2 Method Fig. 2 Phasor Diagram for the current and voltage relationship for resistor and inductor. Fig. 3 Experiment Setup ISBN: 978-1-61804-173-9 14 Latest Trends in Circuits, Control and Signal Processing 1. The setup of the experiment was shown in Fig. 3. Firstly the oscilloscope was connected to the 50Ω output of the function generator. 3Result and Discussion Then, the “Autoset” function of the oscilloscope was being used to display the To make sure the measured value is conform to the output on the screen. The oscilloscope was actual value, two commercially available inductor set to measure the amplitude of the input with a value of 10H and 33H respectively were signal as well as the frequency of the input being used to test the system. Both inductors have a signal. tolerance value of 10%. 2. The function generator was adjusted to produce a 10 kHz of sine wave. 3. Then, the output of the function generator was adjusted so that it was generating a sine Table 1 Measured inductance values wave with an amplitude of 2V. It was being Inductance Adjusted Calculated Error shown in Fig. 4. (H) Frequency Value(H) (%) 4. An unknown inductor was connected in 10 430.5kHz 10.67 +6.7 parallel to the oscilloscope and function 33 142.8kHz 32.17 -2.5 generator. As a result, the amplitude of the signal displayed in the oscilloscope was attenuated. 5. After that, the frequency of the function Based on the result in table 1, we can find that the generator was adjusted and observing the errors in measurement fall in the range of the amplitude of the signal displayed in the tolerance value. As such, we can conclude that this oscilloscope. When its value reached 1V, method is working well in estimating the inductance which is half of the original signal value as value of an inductor using merely a function in shown in Fig. 5, this process was stopped. generator and an oscilloscope. 6. Finally, the current frequency of the function generator was read and the inductance value However, this method should only work well by was computed using equation (5). assuming the series resistance of the inductance is very small or negligible. In this experiment setup, the measured resistance value of the inductors using multimeter is 0.2 which is far less than 50 output resistance of the signal generator. So this assumption can be utilized here. If we are considering the series resistance of the inductor, the schematic now is being shown in Fig. 6. With the present of this series resistance, the measured output voltage on the oscilloscope now will be the resultant output voltage of VL and VR. This condition is shown in Fig. 7. When the series resistance value is getting higher, the resultant output Fig. 4 Initialization setup voltage will tend to dispart with VL and approaching to VR. 50 Ohm Rinductor Unknown Function Inductor Oscilloscope Generator Fig. 6 Schematic for inductor with series resistance Fig. 5 Adjusted frequency at 0.5Vinitial ISBN: 978-1-61804-173-9 15 Latest Trends in Circuits, Control and Signal Processing As mentioned in [7], the in order for this measurement to take place.!͆ However, ɀ ͦ the increasing of the frequency certainly not a good solution here. A simulation with an inductance value of 33uH and frequency sweeping from 10 Hz to 250 kHz was done. It was shown in the plot in Fig. 9. The black curve shows the ideal condition with zero series resistance. The phase difference is 90o at small frequency value. After reaching the maximum phase difference, the increasing in the frequency will result in decreasing of the phase difference. Practically, there is an optimal frequency to get the maximum phase difference. With the increasing of Fig. 7Phasor Diagram for the resistor, inductor and internal resistance, the maximum phase difference the resultant voltage output. can get at the optimum frequency is going down. We can say that the increasing the frequency doesn’t By considering the internal resistance of the inductor mean to improve the accuracy in measurement. In and using lumped element analysis and taking the fact, the increased internal resistance will affect the Rinductor = r, the voltage divider rule now become outcome and it cannot be compensated by merely adjusting the frequency supply.