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9v Battery Impedance

Measuring the Characteristics of Depleted Cells


©2015 By Jack Orman

There have been many discussions about how a dying battery can have an impact on the sound of certain fuzz pedals, especially transistor-based circuits that have little or no power supply filtering, and that were designed to run on battery power.

Most claims are for a warmer, smoother distortion sound, and the effect is often attributed to the increased resistance of the battery as it ages.

There are also attempts to duplicate the aged battery characteristics with an AC power supply adapter by inserting resistance in series with the power output connection.

The suggested resistors (or potentiometers) to produce the old-battery-response are usually in the 1k to 5k ohm range. However, there is little research that has been available to provide a guideline for selecting the resistor value, so I decided to collect some used 9v batteries and subject them to a series of tests.

Summary

If you don't feel like reading the whole article and struggling through all of the technical details, I will summarize the results here.
  • Fresh batteries have low DC resistance, 5 to 25 ohms depending on construction
  • Battery resistance is highest at DC and decreases with frequency
  • Even depleted batteries have less than 200 ohms internal resistance
  • Fuzz tone changes with a depleted battery are from the lower voltage not increased resistance

9 Volt Battery Basics

Heavy Duty batteries are sometimes called zinc-chloride cells, taken from their chemical make up. The body is a steel shell that is attached to a zinc electrode which serves as the negative pole. Ammonium chloride or zinc chloride is mixed with manganese dioxide and carbon black paste for the positive. A carbon rod is used as the conductive terminal for the plus side because it will not corrode, and it will be topped with a metal cap or terminal.

Alkaline batteries have a different chemical composition. They still have the steel shell and zinc electrode as the body but the electrolyte in the paste is potassium hydroxide instead of the chlorides used in the heavy duty batteries. The carbon rod may be alloyed with other chemcials and physically shaped to improve performance. The different construction allows alkaline cells to deliver more power for a longer period of time.

The "heavy duty" and alkaline batteries are the most common types used in fuzz pedals. It is rare to see lithium, li-poly or other cells being used so we will only test the two common compositions.

As a baseline, I bought a new package of each type of 9v battery to test as a starting point. These batteries were fresh and had never been used. The method used to measure the DC resistance was to take a reading of each battery with only the input of the Fluke multimeter as a load (10M). Next, load the battery with a known resistance (560 ohms) and measure the voltage again. I selected the 560 ohm resistor since it will produce a modest load of about 16 or 17 milliamps. Ohm"s Law is then used to calculate the internal resistance of the battery that is required to produce the voltage drop (the difference between the loaded and unloaded measurements).

9v Battery Brand DC Resistance in Ohms
Sunbeam Heavy Duty #1 25.28
Sunbeam Heavy Duty #2 26.57
AC-Delco alkaline #1 5.99
AC-Delco alkaline #1 4.82
As expected, the alkaline batteries have a lower DC resistance than zinc chloride "heavy duty" types.

Measurements of Used Batteries

I have a box of used 9v batteries on my bench that I had saved for testing. I labeled the batteries 1 though 7 but once the test was underway, I had to discard #4 as being too depleted for reliable functioning. A different load resistor was used in these tests.

9v Battery Brand Unloaded Voltage Loaded Voltage DC Resistance in Ohms
AC-Delco Heavy Duty #1 9.49 9.08 37.91
Rayovac alkaline #2 8.92 8.77 14.60
Sunbeam Heavy Duty #3 9.78 9.47 27.33
GI Heavy Duty #5 9.12 7.54 188.40
Duracell alkaline #6 7.73 6.43 195.00
Golden Power Heavy Duty #7 9.02 7.91 78.47
All of these 9 volts have been used periodically for bench testing and the #5 & #6 batteries in the table are pretty well depleted. You can see the voltage sags quite a bit once the battery has a load on it. Even depleted and at a lowered voltage, the DC resistance of the used batteries is less than 200 ohms.

Impedance at AC Frequencies

I modified one of the AMZ multi-purpose opamp boards to serve as a fixture for testing the battery impedances at AC frequencies to compare to the DC results.

The test method was presented in a paper by Ranganathan, Faruque, and Schultz of the Department of Electrical Engineering at the University of North Dakota, and the circuit worked well.

A frequency generator provided a sine wave to the test board and the RMS voltage was measured at two places on the test rig to provide the numbers used to calculate the impedance.

Battery Brand Impedance at 220 Hz Impedance at 1k Hz
Rayovac alkaline #2 0.76 --
GI Heavy Duty #5 145.73 135.82
Duracell alkaline #6 40.36 38.55
Notice that the AC impedance is less than the DC resistance, and the AC impedance decreases as the frequency increases because the internal capacitance of the battery begins to have an effect.

Low Current Class A Circuits

Almost all of the pedal circuits recommended for use with a depleted battery or the voltage sag circuit are Class A amplifier circuits with low current requirements. I measured the idling current draw of several circuits of this type:

Circuit Current Use in milliamps
Jfet Buffer 0.54
Mosfet Booster 1.16
Mini-Booster 0.53
Fuzzface 1.38

I also measured the current of the first 3 circuits with a 1v audio signal passing through them, and there was no change in the current draw, as was expected.

Since the current requirements of these transistor circuits are so low, the battery is not under a heavy load and the voltage sags very little. For example, the partially depleted Golden Power heavy duty 9v battery was still above 9v when connected to any of the circuits.

The resistance of the battery will not have a major impact on the sound. What will have an impact is the lower voltage that results from the reduced amount of active chemcials in the cell.

Voltage Sag Circuit

It is trivial to design a circuit that imitates the voltage loss and increased battery resistance. A series diode and resistance will do a good job of imitating the effects of a used battery. The diode introduces a loss of about 0.7v and the resistor imitates the increased battery impedance.

By placing these two components in series with the positive power supply connection to the circuit, you will have a good imitation of the used battery effect.

For more voltage drop, place two 1N4001 diodes in series instead of just one, and increase the resistance to 220 or even 470 ohms.

Connect the voltage sag circuit to your transistor fuzz or booster circuit, and enjoy the warm sound of a depleted battery (imitation).

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