Battery Life

Saturday, June 21, 2008

Author's Note: The bench test described here was for a previous version of this amplifier circuit. Since the battery life for the new version is approximately the same, I haven't repeated the tests.

Can you make money as a street musician? Not if the coins in your guitar case don't pay for the batteries in your amp! Let's crunch the power supply numbers for the Street Musician Amp. Each 1T4/DF91 demands 50mA of heater current at 1.4 volts, representing a power load of 70 milliwatts. A 3S4/DL92 requires twice as much power. To put this in perspective, a single 12AX7 draws 300mA at 6.3 volts, representing almost 2 watts! It's strange to think of the 12AX7 as a power hog. Energy consumption depends on your perspective.

The heater load on the D cell is 350mA. The 9-volt batteries are subjected to plate current of 7mA at idle and 9mA at maximum overdrive.

Alkaline battery capacity data posted to the web is extremely inconsistent. Why don't our favorite battery manufacturer's post their data sheets? I'll pick some potentially bogus prognostications from questionable sources at random and try to predict the amplifier's battery life. If we assume a 9-volt alkaline battery has a capacity of 300 milliamp-hours, then in this amp they last 43 hours for clear, crisp, country twang and 33 hours for transcendental, Timothy-Leary, In-a-Gadda-da-Vida, belly-button exploration. If we assume a D cell can supply 6.5 amp-hours, then it holds up for 26 continuous hours.

There's only one way to conclusively determine how many coins need to drop into our guitar case per day to pay for batteries. I'll purchase some fresh, off-the-shelf alkaline, make some measurements, and dump the sacrificed carcasses at a local German food store where they have convenient containers for ecologically responsible battery disposal (a shameless environmental plug, I'll admit).

I've got a D cell and five 9-volt batteries, all newly purchased from three reputable manufacturers. (To avoid having to sit in front of a microphone with my attorney present I won't mention the brand names.) I've set my signal generator and the amplifier's controls to put the amp into slight overdrive, simulating a 12-bar progression with just a little grit and sizzle.

Instead of a speaker I'm using an 8-ohm dummy load. (My "dummy load" is actually just a 1/2 watt resistor. This isn't a 70-pound stage amp - even the 7-pin sockets are an easier lift for us old folks.) I want to state up front that my avoidance of a real speaker is not a reflection of a lack of appreciation for the musical talent of my signal generator. It's just that a little more variety than a 600-Hertz sinewave would be more to my musical tastes.

Let the test begin!

The 1T4 filaments are glowing, not spectacularly like the 100-kilometer long filament of a vintage 80 tube, but it's great to visually experience battery dissipation in action. I can't see through the plates of the 3S4, so the state of the insides are a complete mystery. The preamp tubes are obviously a better choice for the Christmas season.

This isn't encouraging. The voltages have dropped already and my signal generator has been playing for only 60 seconds! Obviously the in-circuit voltage is a bit lower than the open-circuit voltage. My D cell's 350mA load at 1.55 volts represents a load resistance of 4.4 ohms. The 4-percent drop in voltage is caused by internal battery resistance. If we use a simple voltage-divider model of the battery and load, we get an effective source resistance of less than 1 ohm. This is a lot lower than a typical Marshall or Fender power supply. Batteries sure can simplify things. Motorboating? Screen supply sag? Not with this amp! I'm getting more optimistic.

My optimism was a little premature. We're not doing well. The voltages are dropping precipitously. Maybe that 100k grid-stopper in the first stage isn't enough. Perhaps I'm amplifying the BBC and Deutsche Welle in addition to the clean, consistent intonation and sustain of a flawlessly-executed signal-generator solo. No, there's no evidence of RF, but I don't think we'll get a recording contract out of this.

It's been almost an hour and it looks like we're steadying out a bit for the long haul. My signal generator is still hanging in there for the set and hasn't asked for a smoke break yet. It's a Hewlett-Packard Model 651B from the late 1960's. All transistors. I opened it up a few years ago thinking it was time to do some preventative maintenance, like for my Model 410B Vacuum Tube Voltmeter. I was pleasantly surprised by how clean the 651B was on the inside. No dust, no cobwebs, no rodent droppings, no nuclear fallout from Chernobyl or the Bikini Atoll. There's something to be said for a technology that eliminates cooling vents.

Look's like the D cell has dropped below the datasheet spec of 1.4 volts. As the voltage drops the heaters draw less current. That should help. I'm trying to look on the bright side.

Data sheets can be a bit tricky for directly-heated cathodes. The voltage across the cathode varies by 1.5 volts. So we can think of an effective cathode voltage of +0.75 volts relative to where the negative end of the battery is connected. Unfortunately when we use this approach our computations suffer from overcompensation - the data sheets measure electrode voltages, most notably the grid voltage, relative to the negative side of the cathode, not the average cathode voltage. Sometimes it pays not to over-think the problem.

We're feeling the strain now. The batteries are below my design spec and the 45-volt Christmas tree has dropped to 42 volts. My signal generator has been playing at full power for six and a half hours without an intermission - I hope the American Federation of Musicians doesn't hear about this! Our output power is now down to 48 milliwatts, but we still have plenty of stored coulombs to be discoverd by a booking agent, so play on!

End of Day 1. We've survived 8 hours of pushing electrons. Output power has dropped a bit because of the lower plate supply, but it's still enough to resume this public service gig again tomorrow.

Sunday, June 22, 2008

Start of Day 2. Our batteries have had a chance to relax and their voltages reflect it. They're obviously a bit perkier than they were at the end of yesterday's marathon solo act. The Radiotron Designer's Handbook, fourth edition, has an interesting discussion of this phenomenon on pages 1273 and 1274. Langford-Smith reports that the batteries in a radio with a plate supply load of 15mA have greater storage capacity when the radio is played 2 hours per day versus 8 hours per day. We can speculate that as street musicians our public-financial-support to battery-expense ratio increases when we take more breaks and play for shorter sessions. It's an appealing financial strategy.

Looks like Langford-Smith is on to something significant. Cool-hand 651B has been bending that 10th-fret note for an hour but our voltages haven't yet decreased to yesterday's levels. All the bills and coins dropped into the guitar case this morning are Pure Profit.

Strange, the 9-volt batteries are still a tiny bit higher than they were yesterday. Maybe I'm measuring a different one in the Christmas tree today. Here's a quick check of the lot: 8.33, 8.33, 8.32, 8.33, 8.32. Pretty consistent - must be just a measurement error in our favor. Kind of like

the strange effects of power supply ripple

- it's hard to accept until someone offers a plausible explanation.

The voltages are now lower than yesterday. Our free cash flow has ended. Output power has dropped a bit and our constant power amp grid bias is pushing us closer to Class B. The amp still sounds good though.

End of Day 2. A full weekend of playing for food. The D cell is looking a little ragged. The amp still sounds good, but if we try to keep it up for another day on the same set of batteries we're certain to be overpowered by the accordian player at the next cafe.

Let's take inventory. I paid 2.25 euro for the D cell and 5.49 euro for each 9-volt battery. (OK, I was ripped off on the 9-volts, but science is science.) That comes to 29.70 euro. After 16 hours of full-power playing, without a pause to sign a recording contract, my signal generator has burned 1.86 euro per hour in batteries. That translates to almost 3 dollars per hour in the CTA tunnel at O'Hare, which represents a lot of cash on a slow travel day. I better keep my day job.

On second thought, batteries are a lot cheaper at Walgreens on Michigan Avenue...