ESR Meter

ESR Meter - Motivation 

This is an ESR Meter project which I did in Mar 2022.  In my many years as a electronics design engineer, I never needed a ESR meter.  But recently when I was doing some repair work, I realised that I needed a tool to identify bad electrolytic capacitors.  In design work, I always use new capacitor so there wasn't a need for this tool.  So, I decided I should have this tool.  But when I checked the price, I found that it cost too much to buy this tool.  The next possibility was to make it.  I know I could make this but where do I start to begin with.  I decided I should just look at all the DIY designs and see which is the best I could adopt as my initial design to start with.

Let me try to share what I know, and it is always good to understand the concept before looking at details.

Concept 

A ESR meter basically is an AC resistance meter.  A typical multimeter measures resistance with DC. The difference with using AC is that it is able to measure the series resistance of capacitance or more technically called the Equivalent Series Resistance (ESR).  A capacitor can be represented as follows

ESR is the resistance represented as a series resistor with the capacitor C.  

Why do you need AC instead of DC?  Since only the ESR is of interest, the capacitance has to be shorted, and this is done by using AC of a high frequency so that the capacitive reactance is very low since  Xc = 1/(2*Pi*F*C)  where F = frequency and C is the capacitance. When the capacitive reactance is small, the impedance measure will mostly be the ESR.

The AC used is generally in the range of 50Khz to 100Khz, square wave or sine wave does not really matter.

Design Evaluation

I have reviewed many DIY designs but I particularly like the design by Ludens because it is simple and conceptually sound.

https://ludens.cl/Electron/esr/esr.html 

Schematic 1

The design consists of the following

1.  Oscillator - Using Op Amp U1A as a relaxation oscillator to generate 50Khz

2.  Impedance transformation with T1 with a 20:1 ratio.  This basically transforms the reflected impedance of R5 // R6 of 5 ohms to 20*20*5 = 2000 ohms which the op amp will be able to drive.  Quite a simple but smart concept to solve the impedance matching issue to have maximum power transfer,

3.  Amplifier gain with U1B of 39 to amplify the signal (~Vs/20 p-p)

4.  AC to DC conversion with voltage doubler (using C6, D1, D2, C7)

5.  Finally using a ammeter M1 as a voltmeter with R11 in series

Problem with the design

Luden's design above presents some basic design issue

1.  Voltage supply - With op amp TL062, if look at the allow swing for input and output, with supply at +/-15V

Input is allowed -12 to 15 typical, but guaranteed at +/-11V

Output is allowed +/- 13.5V, but guaranteed at +/-10V

This means that the minimum voltage supply must be at least +/-5V, for very low swing of mV range.  To have any meaningful swing, the voltage supply will have to be 5+Swing voltage.  So if you want a swing of 2V peak, you need at least 7V, meaning 4Vp-p swing will require +/-7V (or 14V rail to rail).  Clearly 7V is insufficient, and 15V is barely enough for 2.5V swing (guaranteed swing). 

2.  Gain of U18

The design has a inverting gain of 39.  There are 2 problem with this gain.

a.  With a relaxation oscillation passing through the transformer, the signal at the output assuming low loss transformation will be Vs/20.  Assumming we use 15V, so the rail voltage is 15/2 = 7.5V.  Then the signal will be 7.5/20 = 375mV.  If the gain is at 39, then the output of U1B must be 39*0.375 = 14.625V.  This clearly exceeds the rail voltage of 7.5V, which means output is distorted with flatten output max a 7.5V (if the op amp can even reach that).  But as I said earlier the guaranteed output is at is 2.5V max.

b.  Looking at the gain-bandwidth product for TL062 is 1Mhz, with a gain of 50, the max frequency to pass through with unity gain is 1000/50 = 20Khz.  How is it possible to amplify a 50Khz signal when the gain = 1 at 20Khz?

Clearly, the amplifier gain is not correctly designed to achieve the result.

3.  Metering

The conversion of the AC to DC uses a voltage doubler.  If the signal is already so high, why is a doubler needed?  Is it that there is a high level of attenuation in the earlier stage that make it necessary to use a voltage doubler.  If we are able to create a swing in the amplifer to the max of 2.5V in the prior stage, then there is no necessity to use a doubler, a single diode detector will work as well.  Finally, the meter is not buffered, which will cause voltage droop error which will get worst if a less sensitive meter is used.  Even with 50uA meter the droop error could easily be signifcantly high and will get worst with a less sensitive meter.

What is suspect.

I suspect that there is a significant drop of voltage when the measurement is done, because there is insufficient drive to support it (even with transformer).  This resulted in later gain stage to be increased, but suffer bandwidth reduction, so yet again voltage doubling to get the metering result.  What this means it that there is a lot of errors being introduced when measuring low resistance to higher resistance, because the internal parameter are changing with the load.

New Design

The new design started with several objectives

a)  To solve all the issues mentioned above.

b)  To achieve the performance like a industrial product and yet low cost

c)  Impose design to no more than 4 Op Amps, uses off the shelf parts, and parts that are easily available.

d)  There are specific constrains which I imposed on the design to make it very low cost with easily easily to find parts

1) For example, I could easily find a cheap multimeter with 500uA movement instead of using a dedicated 50uA meter

2) Using a transformer from a AC-DC SMPS (like 230 to 5V USB supply) instead of a specially wound 20:1 transformer.

 With the above consideration, the final design is created progressively.  I said progressively, because this was not done in one go, but after several iterations of issues and resolutions from the understanding of the original design.

The final design was done with the following change

1.  Change the IC to TL082.  This is a needed change to ensure that the swing requirement can be extended, and the bandwidth can be wider.  It is not the best, but definitely better than TL062.  There are at least 2 reasons for TL082.  1.  It has large gain-BW product of 4Mhz. It also has a wider swing allowed which mean a lower Vs can be use.  I use 12V (Vs = 6V) and max output swing is 6-3 = 3V guaranteed.  Actually, I am already pushing a little beyond the quaranteed but defintely within the typical limit since the amp is having a swing of about 3.5V with a separation of 2.5V from Vs.

2.  Raised the operating frequency to 70Khz which is better than 50Khz, I did try to push it to 100Khz, but the performance suffer slightly because it is already hitting the bandwidth limit of the op amp, so it does not offer much gain.  I think it does not make much difference at 70Khz, since the significant square wave harmonics will be more than 200Khz.

3.  I did not use a 20:1 ferrite transformer because I do not have the tools to wind one, so the easiest I can find one is a flyback transformer which is about 10:1.  With that, I expect the voltage at the output to be higher at Vs/10.

4.  The output need to have a strong drive to avoid loading loss which will definitely happen if it is driven directly with the op amp.  Therefore a push-pull stage in included to have a low impedance drive.

5.  Since I can be sure that the output loading loss is minimal, I will need only a gain of 10 to restore the signal at the test point back to the level of the oscillator without causing over drive distortion.  Any loading loss will only cause the signal level to drop lower that the oscillator level, so it will always be safe to use a gain of 10 (same as the transformer 10:1)

6.  To ensure that the AC-DC conversion does not suffer from loading droop due to the meter, a buffered output is created with another op amp.

7.  If a gain of 10 is use, we know that the output swing is already at the max swing possible, then it makes no sense to use a voltage doubler as a AC-DC conversion.  A simple single diode peak detector will be better since we know that the max output will be one diode forward voltage less, meaning the maximum swing can never be exceeded.  One other compelling reason why I use a buffer is because I am using a less sensitive meter of 500uA full scale deflection which will definitely cause bad loading without a buffer.  With a buffer, even a 2mA FSD meter is no problem at all.

8.  I change the original R6 from 10 ohm to 5 ohms, because I wanted a mid scale of the meter to be at 5 ohms instead of 10 ohms in the original design.  Even though it appears that the mid scale should be at 5 ohms, it is not, because of the losses due to the reflected impedance and the resistance in the coil winding, but the error is relatively small.  Actual mid scale tested with 5 ohm without correction is at 47.8% which should be relatively easy to correct to 50%.

Schematic of the final design.

Schematic 2

9.  The design was tweaked as I implement the original design and when testing it I notice the issues and understood them.  The final piece I have to explain is C6 and R14.  This is a snubber circuit that has to be included.  The hard drive from the drive is creating a high voltage during switching such that the voltage swing shoot up to the supply voltage level which is technically not possible if it working correctly.  I found out later that it was cause by the inductance of the transformer that induced the high voltage (due to faradays law V = -Ldi/dt). Given that I know the inductance of the transformer, I am able to compute the value for the snubber.  Once I put the snubber, the voltage overshoot at transition disappears and I get a perfect square wave.

10.  There is one last imperfection, which is quite obvious from the scope.  There is a crossover distortion because of the use of the class-B amplifier driver without crossover distortion correction.  However, I will leave it as it is because I am using a square wave, so this distortion is not serious enough to affect the measurement result.  In fact, after the amplifier stage, the crossover distortion disappears totally for obvious reason.  The amplifier at gain of 10 is already acting as a filter to remove all the high frequency harmonics cause by the crossover distortion.  I also can observe that the square wave after amplification is slight rounded at corners, which confirms my suspicion that the op amp is already operating to its limit frequency.

Final Product

Sorry, every small components used are SMD, so only the transformer and IC are visible

The schematics also shows the actual test value which has a progressive increasing error with respect to the expected actual under idea condition.  The error is actually monolithic and in this particular application as a ESR, it is working in my favour because I am interested in the lower resistance value and would prefer higher resistance to appear worst and respond less.

Design Update

After posting the design, I receive feedback that there is already a design by Jay_Diddy_B (5 transistor ESR meter).  I reviewed the design.  Indeed it is a great design using simple and cheap components to achieve the desired performance. I have even received some nasty feedback that the transformer is not needed. After looking at the design, I did some test and found that the transformer can be eliminated as long as the driver is there. 

I wanted a simple to assemble design which will be easier with op amp than using transistors.  Another requirement is to allow for the use of ammeter of higher full scale deflection (any meter up to 5mA should not be a problem)

The updated design is functionally similar to the 5 transistor by Jay_Diddy_B except for the AC to DC conversion.  I use a simpler diode peak detector which has a range more suitable for op amp design instead of a voltage doubler design.  Also the meter is now buffered so the loading of the meter is no longer a concern.  The mid scale is about 2 ohms.

Schematic 3

For a slightly wider resistance range and slightly higher mid scale of 2.3 ohms, you may use this circuit with a slightly higher drain current of 35 mA.  There reason for this change is to have a wider swing for pin 1 of  U2A so that the result will be more consistent regardless of the choice of schottky diode used for D3.  If this is not a concern for you, the earlier design is just as good.  Note for protection diode D1 and D2, I use a TVS diodes instead of 1N4007.  Any TVS diodes can be used but the ability to absorb the voltage shock depends on its size.

Schematic 4

With Waveform

Trade-Offs Evaluations

1.  Transformer

We know the difficulty of using a specially wound transformer, but what is the advantage of using 1 in schematic 1 and 2?

Transformer provides a more efficient power transfer of test signal for measurement.  Otherwise, using schematic 3 and 4 without the transformer, there is a large power loss at R14.  This resulted in drain current of about 11mA for schematic 2 to about 25mA for schematic 3 to 35mA for schematic 4.  If you intend to power the ESR meter with battery, then it make sense to use a transformer.

2.  Mid Scale Deflection

The ideal mid scale deflection is set by R15.  Ideal mid scale for schematic 2, 3, 4 are 5, 3, 3 ohms.  The ideal mid scale is the max achieveable value, meaning for ideal mid scale of 3 ohms, the maximum measurable at mid scale is 3 ohms.  However, in the actual design, you never reach the ideal mid scale value.  The inability to reach the mid scale reading is because of conversion loss, most notably the loss from AC to DC via diode D3 which is the major contributor.  The purpose of schematic 3 to schematic 4 is to reduce the loss, resulting in mid scale improvement of 2 ohms to 2.3 ohms.  For one who wants a wider reading for low ohms reading, schematic 3 appears to be better, but for an idealist, schematic 4 is closer to the ideal, because the improved reading is a result of larger error contribution.  This would also mean that component selection for D3 is more critical in schematic 3 then in schematic 4.

3.  Error elimination

Can the error in point 2 be removed?  Yes, it can, but will require a precision peak detector which requires another stage of op-amp which I do not intend to put in.

4.  Lower voltage operation

What would you do, if you want to use 9V battery or using 5V battery?

The above uses TL082 which have relatively poor input and output swing which requires the use of 12V supply to overcome this limitation.  Any supply voltage lower than 12V, will require you to choose a op with rail-to-rail capability that allows swing to the full voltage limits for both inputs and output.  Note that whenever the voltage is changed, the wheatstone bridge ratio (R6/R7, R14/R15) has to be changed such that the resulting signal for measurement to the op-amp is at about 400mV p/p (schematic 4 was at 370mV p-p) across the test points.  If you are using battery, I will chose schematic 2 or implement the transformer into schematic 4 for better power management.  Note, any transformer found in small SMPS is usable, there is no need to specially wind a 20:1.  A typical SMPS transformer is about 10:1 which can be tweaked to work by adjusting the wheatstone bridge ratio to achieve the 400mV p-p signal.

5.  What Op-Amp can be used?

The op-amp to be used depends on what voltage you want it to be used.  See point 4.  But there is another requirement which must be satisfied, and that is the gain-bandwidth (GBW) requirement.  It need to have a minimum gain-bandwidth product of 2 MHz.  TLC2272 would have met the rail-to-rail voltage requirement, but limited by its gain-bandwidth product of 2Mhz. LF351, LF247 or LF357 will be somewhat similar to TL082.  Another common op-amp LM833 is a better choice than TL082 and will give you better frequency performance.

Test Data

To map the ESR to the deflection scale of the meter, test has to be done at various test resistance.  The values marked yellow are value obtained by testing.  Values that are not highlighted are extrapolated from the test results so that the scale can be computed.

Meter Scale

The meter scale assumes that the voltage will give a proportionate deflection which should be the case for moving coil type meter deflection.  The scale image can use by scaling it to the right proportion for the actual meter.  The marker below is the rotation center line, position at the center of the meter.

Actual Meter

The scale is first printed on paper and check for size matching with the actual meter.  Scale the image of the meter scale until it match the actual meter.  Next use the existing metal scale plate on the meter and paste the printed scale on the reverse side.  Make sure that the center of paper scale and the meter scale matches.  What I did was to position the plate over the paper scale and draw the plate outline on the paper and also the mounting holes.  I manage to get this done in one attempt.  There is slight mismatch on the needle and the needle rest point which could be adjusted on the meter.  Tested on the data test points and the reading error is within 5%, so it is not a big concern.

Final Schematic

The final circuit is tweak further to widen the scale in the lower ohm region.  This is done with 

R15 decreased to 2.2 ohms and also R14 raised to 100 ohm, so that the current driving the test point is reduced.  With that, the attenuation is increased to (1/45).  This means the gain after this stage should have a gain of about 45 to compensate for this loss of signal level.  The differential amp gain is raised to 22 and buffer driver gain is raised to 2, making a total gain of 44.  The bandwidth for the differential amp is reduced by 2.2x, but this is still ok for 100khz, since the total Gain-BW = 100k * 22 = 2.2Mhz which is still within the specification of TL082.

Final Scale

The final scale use is as shown below.  The mid scale is now at a tag below 2 ohms

Questions to think about

1.  Should you use square wave or sine wave for the oscillation? 

2.  How do I set the mid scale deflection to a different value?

3.  What are the AC to DC conversion techniques and which is the best for this application (given the impose constrains)?

4.  What modifications are needed, if I want to operate from a 9V battery (with a least 7V)? 

5.  Where was the error in the reading introduced and how can we have a design with smaller error?

Note, some of the questions are already answered in the trade-off evaluations.