Projects:2019s1-135 A Low-Cost Impedance and Transfer Function Analyser Part 3

Introduction

Traditional impedance analyzer such as Hioki IM3570 is expensive in the market which costs about $12,000. In 2018, an impedance analyzer was made but it is slow and inaccurate at high frequency. Therefore, this projects aims to create a low cost impedance and transfer analyzer which has high accuracy, cover wider range of frequency, and affordable for student lab use.

Project Team

• Yuqin He
• Pei Ying Lim

Project Supervisors

• Keith Kikkert
• Wen Soong

Objectives

An impedance and transfer function analyzer with

a) accuracy <1%

b) Bandwidth of 1Hz to 1MHz

c) low cost (value for money)

Background

Fundamental theory

This impedance analyser uses the concept of voltage divider

Voltage divider is shown in diagram below:

voltage divider

From voltage divider rule,

𝑉𝑏=𝑉𝑎*𝑍𝑢𝑛/(𝑅+𝑍𝑢𝑛)

If 𝑅=𝑍𝑢𝑛, then 𝑉𝑎=2𝑉𝑏

When we get maximum output power, it will be easier to detect the Vb and hence better accuracy.

Implementation Design

Based on the voltage divider rule, we design the hardware as shown in the diagram above

Comparing with last year project, firstly, we use the Digilent Analog Discovery 2 which has embedded FPGA, analog to digital converter and waveform generator.

Additionally, we implemented double-pole double-throw relay connected in series to reduce the amount of relays required to control the reference resistors.

We also reduce effect of stray capacitance and inductance by reducing the amount of the resistors and shorten the length of track through the design of the PCB board.

Calibration

Apart from obtaining higher accuracy through the design of hardware, we also implement the calibrations from software to calibrate the results in high frequency.

The calibration includes three parts: Gain calibration, short-circuit calibration and open-circuit calibration

For Gain Calibration, we firstly connect the signal generator to analog digital converter,

We can then obtain the Voltage correction factor 𝐾=𝑉b/𝑉𝑎 and Phase correction factor = phaseB - phaseA

For Short-Circuit Calibration, the diagram is shown on the below:

By switch off short-circuit contact of the relay, we can obtain the stray inductance in the circuit.

Then extract the stray inductance value out of the measured impedance to compensate the inductance exist in the track of the hardware.

For Open-Circuit Calibration, the diagram is shown below:

As it is shown, the Open-circuit is used to compensate the stray capacitance which includes capacitance form switch relay and PCB, cables and oscilloscope.

Result

Impedance Analyser Result

The measured results of impedance are shown in the diagram below:

As it is shown, the measured results of the impedance under 100 Ohms are with good accuracy.

while in higher frequency, the larger value of impedance under test will decrease sharply which is resulted from the stray capacitance.

After implementing the software calibrations, the results are almost a straight line within the proposed frequency range.

The test frequency range is 1Hz-1MHz

The accuracy is within 1% and the operation time is only several seconds, which is much better than previous system.

Transfer Function Result

By connecting Vb to Analog Digital Converter, the result is shown in the diagram below.

The result is expected to be 1 under the frequency range 1-1MHz.

before Calibration, the result is around 1, but after implement the Gain calibration, the result is exactly 1.