**The ALICE Impedance Analyzer**

ALICE 1.1 Desktop is a multi-purpose and incredibly useful tool for working on electronics projects and experiments. But with all its capabilities it can be a little intimidating to get comfortable using all of the tools. In past Blogs we have explored the SMU and how to make current measurements. In this Blog entry we are going to go over another of those many features (The Impedance Analyzer) so that you can get the most out of this powerful software.

**When would you use an Impedance Analyzer?**

If you are working on a high speed application or with specific frequency requirements, you might need to take into account something known as parasitic elements in your circuit. If you are unfamiliar with this term, a Wikipedia definition can be found here.

Often the markings on small components like the ones found in the ADALP2000 Analog Parts Kit are very difficult to read and measuring the actual value with the impedance analyzer can confirm that you have selected the proper component for your circuit. Or you may want to reuse some components you have removed from some broken or no longer used piece of electronics. Verifying their values and to test if they are still good, the impedance analyzer can be a very handy tool.

The impedance of a component or combination of components is the total counteractive force to the flow of electrons through. This can be thought of as the resistance of the circuit component and can be measured with an impedance analyzer. But if impedance is just a way of representing the resistance a circuit offers, why is a special tool required and not just a digital multimeter? The reality is that no real components, resistors, capacitors, or inductors, are purely resistive or reactive. Every component in reality is a combination of R, C, and L elements. Hopefully, one of the three, R, L, or C dominate the others, the usually small unwanted parts are called parasitics. In fact some DMMs do have functions that measure capacitance and inductance but almost never measure the parasitic terms. They also only test at a single fixed ( or a few ) frequency,

The Impedance Analyzer can provide information pertaining to impedance, inductance, capacitance, phase, and quality factor Q, or dissipation factor D, of the network. It is available in the ALICE 1.1 Desktop software for the original ADALM1000, or ALICE 2.0 Desktop for the new ADALM2000, and a detailed description of how to measure a simple low pass filter is included on the ALICE User's Guides on the Wiki page.

**Background:**

The basic concept that is used to make gain/phase, impedance and RLC measurements using ALICE Desktop is shown in figure 1. Channel A of the ALM1000 is used to apply a known frequency sine wave at VA and measure the applied voltage waveform. Channel B is used to measure the voltage waveform seen across the network under test. FFTs are calculated on the two waveforms which provide amplitude and phase information at the applied frequency. From these the relative gain (CHB amplitude / CHA amplitude) and relative phase ( CHB phase – CHA phase) are obtained. Further these values can be used to calculate the impedance (series RLC) of the network in the dashed box.

The resistor, R_{EXT}, is a known value. For the audio frequency range measurements possible with the ALM1000 hardware it can be adjusted as needed depending on the magnitude of the impedance being tested. Impedances in the range of about 0.1 to 10 times R_{EXT} can be accurately measured. R_{EXT} can range from 50 Ω to 50 KΩ.

The unknown impedance to be measured is modeled as a series circuit consisting of an unknown series resistance, R_{X}, and an unknown series reactance, jX_{X}. The magnitude of the impedance is Z_{X}.

Figure 1: Basic Concept

Three voltages are measured:

- VA is the applied voltage (from Channel A of the ALM1000).
- VZ is the voltage across the unknown impedance (from Channel B of the ALM1000).
- VI, the voltage across the known resistor R
_{EXT}is calculated from VA and VZ and is related to the current in both R_{EXT}and the unknown impedance.

These three voltages are actually vectors and indicated in figure 2.

Figure 2: Vector Diagram

Using the law of cosines and referring to figure 2 the magnitude of VI can be calculated as:

The angle Φ is the measured relative phase between channel B and channel A. The law of cosines is used to calculate the cosine of the angle, Θ.

The magnitude of the total impedance (including R_{EXT}) can be calculated as:

We note from figure 1 that the sum of R_{EXT} and R_{X} can be found by:

Thus, we can solve for RX by:

Taking possible measurement errors into account it is possible that R_{X} could compute to be a negative value which is not likely to be the case. The thing to do if that happens is to set R_{X} to zero. The impedance is purely reactive.

The magnitude of the unknown impedance can be calculated as:

The magnitude of the unknown reactance can be calculated as:

Again taking possible measurement errors into account it is possible that the square root of a negative number might occur. If that happens then XX should be set to zero.

Once we have a value for X_{X}, we can calculate either the series capacitance ( when X_{X} is negative = X_{C} ) or series Inductance ( when X_{X} is positive = X_{L}).

**Making Measurements:**

Connections to the ALM1000 and the network to be measured are shown in figure 3. In this case we show a simple series connected resistor and capacitor. R_{EXT} is 1000 Ohms and the series resistor R_{S} is 100 Ohms and the capacitor C_{S} is 220 nF. The channel A AWG generator output should always be set to be in source voltage mode (SVMI) and with a sine wave shape. The user can control the output voltage amplitude and offset with the Min and Max entry slots as when using the scope and spectrum analyzer displays. A good place to start is with Min set to 1.086 and Max set to 3.914 which produces a 1 Vrms amplitude centered on 2.5 V DC. The Channel B analog input is set in the Hi-Z mode when using the Impedance Analyzer and it always considered as an input. The test frequency is set from the AWG controls for Channel A. For this example we will use 2000 Hz.

Figure 3, Measurement setup

The current low level ALM1000 software used in ALICE 1.1 only outputs signals as single shot bursts when the analog output signal is being sampled. The Sync AWG check box must be checked if you are using the ALM1000 function generator output as the applied signal source. If you are using an external signal source rather than CH A the box should not be checked. This will keep both channel A and B in a high impedance voltage measurement mode while capturing data. Next you will open the Impedance Analyzer Window in ALICE.

**Impedance Analyzer Window:**

The main impedance analyzer window should appear, as in figure 4.

Figure 4, ALICE Impedance Analyzer window

It is sub divided into 2 sections. On the right are a number of controls. The most important ones are to set the known external resistor value and the Ohms per division of the plot. In the main graphics section there is a polar plot of the complex impedance with the real part (resistive as the green vector) and the imaginary part (reactive as the red vector). Additional information about the network response is displayed next to the polar plot. If the impedance is negative it is considered to be dominated by capacitance and the calculated value along with the dissipation factor D, in percent. If the impedance is positive it is considered to be dominated by inductance and the calculated value along with the quality factor Q.

Once you have adjusted the relevant settings it is time to hit the Run button and test the circuit.

The examples in the User Guide go on to show the results of testing at different frequencies and also how to measure the input capacitance of the ALM1000 channels.

Hopefully this overview is enough to get you familiar with using this useful tool. If you have any additional questions please head over to the Virtual Classroom section of the EngineerZone Forum.

As always I welcome comments and suggestions from the user community out there on how to improve ALICE.

Doug