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Logarithmic DC voltmeter.



A logarithmic analog DC voltmeter is quite unusual, but very useful.
As it will display from around 100 µV to 20 V on a single scale it will allow you to find short-circuits on the power supply on large boards without cutting PCB traces.
I built this the first time around 1985 with LF356 OP-AMPs. I will not recommend that - you need an offset adjustment on the front panel.
Todays OP-AMPs have much better temperature stability than the LF356, so adjustment can be done once and for all.
This kind of meter is designed for convenience, not accuracy ( which is around ±25% ).
The only hard-to-get component for this circuit is a well-damped meter movement in a decent size.

Meter movement.

The meter movement needed for this design must have zero at the center, a sensitivity of ≤1 mA at less than 0.5 V for full scale deflection.
As we need to redraw the scale, a type with removable face plate is required.
If you buy the movement from new, the coil resistance and full-scale current are normally specified.
If not, you will have to measure it. Do NOT use an ohm-meter - see Appendix A.

You will find such movements in the catalogs of several manufacturers, but those I asked do not stock them so you will have to buy a whole batch.

Another source is surplus sales, but I do not accept the terms of payment ( such as Western Union - up-front of course ) of those I have contacted.

Marine battery charge-discharge meters are another option, but like everything for boats, these are expensive.
Most of these are 1 mA, 50 Ω movements with an external shunt and would be perfect for this.
You may find these second-hand, but they are often "well-used".
Some are glued or welded together, making it difficult to modify the face plate.
I have seen a few where the shunt was mounted directly on the movement. Stay away from these as the case is normally cracked after supporting two 25 mm2 to 50 mm2 wires.

Another option is lab instruments for educational use, but these often use the case as part of the movement, so you are stuck with the case they are supplied in unless you are prepared for some mechanical work.
A web search for "J0409 galvanometer" will list a number of suppliers for these.
These meters are very cheap and you get what you pay for.
They may still be useful for this application with the limitation that for readings below ⅓ full-scale you may have to tap the case to get the proper reading.

I have built and tested the circuit with a Neuberger movement I got from a friend.
I intended to build one with a J0409 meter too, but got so tired of tapping the meter to get a reading.


LV01 circuit schematic.
Fig.1: LV01 circuit.

U1 is a voltage-to-current converter ( a Howland current pump - see [2], [3] ) that supplies 10 mA for a 20 V input.
It is used to increase the input impedance and - to some extend - cancel the input offset voltage of U2.
The circuit around U2 is a logarithmic current-to-voltage converter that drives the meter via resistor RM.
The log-function can be either 2 transistors ( Q1 and Q2 ) or 2 diodes ( D1 and D2 ). The simulation below shows the difference.

Log characteristic of BC846, BC856 and BAV99.
Fig.2: Log characteristic of BC846, BC856 and BAV99.

Log characteristic of BC846/BC856 pair and BAV99 diode as my simulator guessed it.
The x-axis is Vin in fig.1 and the current through the log element.
Left axis is the output voltage from U2 and the right axis is the meter deflection for a meter with 45 degrees full-scale deflection.
Operating the BC846/BC856 pair below 5 nA at room temperature is unrealistic.
Using the diodes has some advantages over the transistors in this circuit:
The 2 diodes are on the same chip so their current/voltage characteristic will be identical and they are at the same temperature.
A larger part of the meter scale is used ( 35deg for the diodes vs. 20deg for the transistors ), making it easier to read the meter.


LV01 signal schematic.
Fig.3: LV01 schematic.

M1 is a meter movement with zero in the center. It should have a full-scale current of ≤1 mA. The full-scale voltage across the meter must be ≤0.5 V.
The current through M1 is set by resistors R11 and R12. Table 1 below list the values for different movements.
The full-scale output on node C is around 0.7 V.
R12 should be adjusted for a full-scale input of 20 V.

The circuit around D2A and D2B is a bi-polar log-converter.
Its upper limit is selected at 10 mA where the self-heating of D2 and U2 is around 1 °C.
The theoretical lower limit of the log-converter is determined by the leakage current of D2, U2s bias and offset current or where U2 runs out of loop gain.
U2 is a low-bias current OP-AMP ( typically ±0.2 pA ) giving the circuit a reasonable log conformance from around 50 nA to 10 mA input current.
R15..R18 is an offset adjustment that injects ±25 nA into point A. This should be adjusted for 0 V output with the inputs shorted. A value of ±5 mV on node C is realistic.
The voltage gain of the circuit from A to C is in the order of 95 dB to 130 dB, so careful physical design is mandatory.
If you want to build this circuit on strip-board, the nodes labeled A and B should be in free air.
If you make a PCB, the nodes A and B should have a guard-ring connected to GND.
Measurements on the unmounted prototype boards shows a resistance of around 15 GΩ from A and B ( in parallel ) to GND.
R9 and C4 is a low-pass filter that reduce U2s upper frequency to around 150 kHz at low gains.
R10 is selected so the output of U2 is just before clipping when when M1 is at full scale. This will reduce the power dissipation in U2, giving better DC stability and prevent the movement from being overdriven.
C6 is optional damping for M1. This is a 1206 case, so up to 47 µF can be fitted.

The circuit around U1 is a Howland current pump. This is necessary to compensate for U2's input offset voltage ( 40 µV typ, 150 µV max ).
U1 is a low-offset voltage ( 0.9 µV ) chopper stabilized OP-AMP. I does have somewhat high offset and bias current so the impedances around it must be kept low.
For best performance, the resistances must be matched. This is most easily done by taking the resistors from the same tape ( R1, R2; R3, R4; R5, R6 and R7, R8 ).
C3 and C4 are required by the LMP2021 - see data-sheet.
C1, C2 is a low-pass filter for the input. With the values shown, the cut-off frequency is around 65 kHz.
Q3 and Q4 are input protection diodes. These have considerably lower leakage current than BAV99 diodes ( I can not measure the actual value, but in a bridge set up with 10 mV across and 10 MΩ in series they came out as a clear winner ).
I tested BAV99 and the base-emitter and base-collector diodes of BC846 and BC856.

The circuit in fig.1 must be built in a closed, shielded box. In this design, I have made the box from PCBs.

For some reason, people always want to use other OP-AMPs than I suggest.
For both OP-AMPs, go for highest possible open-loop gain and lowest possible offset-drift with temperature.
U1 must be able to supply 10 mA and should have the lowest offset and bias voltage you can get.
U2 must be able to supply 10 mA plus the current required by M1 and should have the lowest offset and bias current you can get.
Please do not mail me if you have problems with other OP-AMPs than the ones suggested.

LV01 supply schematic.
Fig.4: LV01 voltage regulators.

±2.5 V regulator, This will run from a 9 V battery. Minimum input voltage is 7.5 V.
With a supply current of 11 mA ( 21 mA at full scale ), this should give a service time of 10..20 hours from an alkaline battery.
I originally used a LM358 for U21, R24 = R25 = 10 kΩ and C25 = 10 µF, but it oscillates unless R22 and R26 are increased to around 100 Ω, increasing the minimum supply voltage to 8.5 V.
I tested the circuit with an OPA1678, but this also oscillates.
An OPA2134 is stable in this circuit, probably due to its very low output open-loop impedance ( 10 Ω at 10 kHz ).
Do not attempt to power this meter from a mains power-supply. The leakage current in the transformer may severely affect the measurements.
Do under no circumstance attempt to power the meter from a class-II switch-mode power supply ( aka USB-supply ). Its noise suppression ( typically a 470 pF to 2.2 nF capacitor between primary and secondary ) may destroy the input circuit and possibly also the circuit you attempt to test.
R20 and D21 are reverse voltage protection for the battery as the battery-holders I have do not include this. In case of reverse voltage, R20 will open.
R21 and D22 is a 5 V regulator buffered by U21B.
R24, R25 and U21C supply 2.5 V which is the meter ground.
D1 and D4 protects U1 and U2 against reverse voltage and over voltage. I do not know if this is necessary, but U1 and U2 are quite expensive so it is a cheap insurance.
The terminals BM+ and BM- connects the meter movement across the battery for battery voltage test.
Select R31 for a full-scale reading of 10 V.

LV01 complete meter schematic.
Fig.5: The complete meter with a 3-position rotary function selector.

Meter with 3-position function selecter: Off, battery voltage and measure.
The movement is shorted in the Off position as transport protection.

LV01 complete meter schematic.
Fig.6: The complete meter with 2 DPDT slide or toggle switches.

Table 1: Suggested component values for different meter movements.
Meter full-scale currentMeter coil resistanceR11R12R31Remark
30 µA100 Ω18 kΩ10 kΩ330 kΩJ0409 data-sheet
487 µA364 Ω820 Ω500 Ω20 kΩJ0409 measured
50 µA2.6 kΩ9.1 kΩ5 kΩ200 kΩFrom supplier catalog
50 µA2.8 kΩ9.1 kΩ5 kΩ200 kΩNeuberger measured
100 µA640 Ω5.6 kΩ2 kΩ100 kΩFrom supplier catalog
200 µA220 Ω2.7 kΩ1 kΩ51 kΩFrom supplier catalog
500 µA135 Ω1 kΩ500 Ω20 kΩFrom supplier catalog
1 mA35 Ω560 Ω200 Ω10 kΩFrom supplier catalog
1 mA50 Ω560 Ω200 Ω10 kΩMarine ammeter

Use the spread-sheet LV01_Calc.ods to calculate the values for other movements.


All resistors and capacitors are 1206 cases ( 0805 can be fitted ).
C1, C2, C5, C24, C26 are NP0 types with a voltage rating of 50 V or more.
All other capacitors are X7R types with a voltage rating of 16 V or more.
D21 is a 1 A diode in a DO-214AC ( SMA ) case. The type suggested has a voltage rating of 200 V, but 50 V is sufficient.
Other diodes and transistors are SOT-23-3 cases.
U1, U2 are SOT-23-5 cases and U21 is a SOIC-8 case.
Except for U1, all SMD components have larger-than-normal pads for easy hand-soldering.
U1's pins 2 and 3 have reduced pad-size to allow room for a guard-ring.
R11 and R18 are universal footprints that will accept a 2.5x5 mm or a 5x5 mm lead pattern 10x10 mm trimpot type.

Modifying the meter movement.

Before you even think about taking the movement apart, you should build and test the LV01 board and the test attenuator shown in appendix B.
First, LV01's offset adjustment is set so the output is as close to 0 V as possible with the input shorted.
You can do this with a voltmeter or with the movement you are going to use.
Wait at least an hour after you soldered on the PCB before you attempt to adjust the offset.
The offset adjustment does not respond very fast, so when you set it, you will have to wait 5..10 minutes to see the final result.
It is possible to set the offset so the output voltage remains within ±5 mV ( there is some VLF noise ).
When this is done, apply 20 V to the input and trim the full-scale potmeter.
Apply the voltages from the test attenuator to the LV01 input one at a time for both polarities and read the meter.
Put the meter readings into the NeugergerScale-sheet in LV01B.ods ( this will give you a symmetrical scale with an average value for positive and negative readings ).
Take the movement apart and remove the faceplate. Measure and enter its mechanical dimensions in the spreadsheet.
If you use a movement with ±45 degrees deflection, you may be able to scale the example faceplate in the download.
Use your favorite drawing program and draw and print a new faceplate based on the data from the spreadsheet.
If the faceplate is reversible ( most are ) put the new scale on the opposite site of the original scale with double-adhesive tape.
Reassemble the movement.
Put everything in a box.

LV01 PCB photo.
Fig.7: Photo of the finished meter with power applied and shorted input.
The measurement range is 100 µV to 20 V.
The scale goes to 1 µV for cosmetic reasons. I will probably leave the 1 µV marks out if I make another one.


LV01 PCB photo.
Fig.8: Photo of the mounted PCB. The size is 56x46 mm.

I have boards available for this project. See the PCBs page.


LV01B design files.

Known Issues / updates.

No known issues.

Appendix A: Measuring the meter movement.

Measuring the meter movement schematic.
Fig.A1: Movement measurement setup.

Fig.A1(a) is used with an adjustable supply and fig.A1(b) with a battery and a potmeter.
Select R1 = 5 / FSC, where FSC is the meter's full-scale current.
If you have no idea what the FSC is, start with R1 = 330 kΩ. This is safe for movements with an FSC of 30 µA.
Adjust Vin or P1 for meter full-scale deflection. If this is not possible, reduce the value of R1 by factor 2 and try again.
If you end up with R1 < 10 kΩ, the movement is not suitable for this design.
While the meter is at full-scale, measure V1 and V2.
FSC = V1 / R1.
Meter coil resistance = V2 / FSC.

Appendix B: An attenuator for testing the meter.

LV01 test attenuator schematic.
Fig.B1: An attenuator for testing the meter.

This is the attenuator I used for testing the meter. The "10V in" terminal is from an adjustable power supply and the terminals 10V..1uV are the outputs to the meter.
See [4] for calculating this type of voltage dividers.


[1] Robert A Pease: Troubleshooting Analog Circuits. ISBN 0 7506 1632 6
A must read. A logarithmic current meter is described.
[2] Texas Instruments: AN-1515 A Comprehensive Study of the Howland Current Pump.
This was written by Bob Pease, but for some reason TI have removed the author from the document.
[3] Howland current pump.
[4] Resistive ladder divider.

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E-mail: diy@poulpetersen.dk

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