# Driving the 4 ohm Load

*by Pat Brown*

## Amplifier power ratings are good for window shopping and water cooler chats. If you need to drive a real-world 4 ohm Load, you need the matrix.

Long ago, 8 ohms was established as a practical impedance for a loudspeaker. If made higher, it gets more difficult for the amplifier to force current through the loudspeaker’s voice coil to make it move. If made lower, the amplifier may run out of current, since the load impedance is the primary limiting factor for current flow. While many other impedances are possible, 8 ohms is a historically-supported value used by loudspeaker and amplifier designers. It also happens to be the resistance that will draw approximately 15 amps of current from a 120 Vrms household electrical circuit, so it represents the minimum numerical load value (maximum load) that 120 V 15 A utility power circuit can drive. Most amplifiers have no problem driving 8 ohm loads, but in special applications that use lower impedances, a closer look is needed.

**The General Concept**

A major decision for the amplifier designer is available current, both in amount and duration, and higher current means higher price. This financial reality provides a motive for limiting the value.

**A Specific Application**

*Photo 1 – Caverness spaces need a lot of sound power for acoustic testing. The sound power level (L _{W}) is an important specification for acoustical test loudspeakers. Shown is Hinkle Fieldhouse in Indianapolis, IN. Testing in this space is what motivated me to look for a better way to drive the the test loudspeaker. The “200 watt-per-channel” amplifier I was using could not drive the load(s) while maintaining the integrity of the sine sweep.
*

The loudspeaker is an Outline GlobeSource^{TM} (GS) radiator – a premium “dodecahedron-like” loudspeaker. The published rated power handling is 1600 W continuous, a rather nondescript rating since the 12 transducers are divided into 4 channels. There are 4 circuits of 3 loudspeakers each, so the one-number power rating presumably translates to 400 W per circuit, each rated at 4 ohms. Plugging these values into the power equation suggests that that each circuit can handle 40 Vrms, and since the objective is to produce as much sound power as possible I need to consider driving it to near that value.

_{RMS}for a sine wave signal. I have concerns about hitting the GS with a continuous signal of that magnitude without some further investigation. It’s an expensive device and the replacement parts come from Italy.

**Getting the Details**

*Figure 1 – The magnitude of the load impedance for each GS circuit. Why are they different? That requires a different investigation.*

_{MAX}) that one circuit can handle is 22 V

_{RMS}. There is no doubt that it can handle more for a short burst waveform, but my intent is to use a sine wave and I have to design for that. That’s nearly 6 dB below the 40 V

_{RMS}suggested by the power rating, so my closer look probably kept me from smoking the GS.

From these tests I now know that I need four amplifier channels that can simultaneously produce 22 V_{RMS} into 4 ohms for at least 14 seconds with stable amplitude over that span. My space budget (it’s a portable system) is 2 rack units (RU). The power equation suggests a minimum amplifier power rating of 121 watts into 4 ohms will do the job.

*Figure 2 – The room testing loudspeaker consists of 12 transducers spread over 4 circuits. Each has a rated impedance of 4 ohms. Driving it with 22 V*

_{RMS}mandates 5.5 A_{RMS}of current from the amplifier. That’s 121 W continuous, since W = EI.**Amplifier Ratings**

Three major variables that must be addressed by amplifier designers are

- Output Voltage
- Output Current
- Output Current Duration

*Figure 3 – All of these batteries can produce 1.5 VDC. The difference is into “what load” and “for how long?” This is why they are rated in mAH (milliamp-hours). Somehow audio power amplifiers have evaded this detail.*

**The Contenders**

**Amp 1**is a 4-channel 1 RU convection-cooled unit. It is rated at 80 watts/ch into 8 ohms, and 150 watts/ch into 4 ohms, with all channels driven. At face value this appears to exceed the 121 W needed to drive the GS.

**Amp 2**is a 2-channel 1RU convention-cooled unit rated at 200 watts/ch with both channels driven. My application will require 2 units, but that still fits my 2 RU size limit. The rated power is the same for 16, 8, and 4 ohms. This suggests that the output voltage is load-dependent – the result of an “only the power matters” design philosophy. Given the shape of GS impedance curve, this behavior may be a deal-breaker for driving it with a 14 second sine sweep.

**Amp 3**is a “multi-mode” amplifier with 8 channels that can be used independently or combined in various configurations. The mode that looks most promising for my application is the use of 2 channels to form a single amplifier with increased current output. That would give me 4 channels with solid 4 ohm performance, packed into 2 RU. But, I need to know whether the 4 channels can be driven simultaneously with a sine wave to 22 V

_{RMS}when loaded to 4 ohms when fed by a single 15 amp utility power circuit. Multi-channel amplifiers can run out of current when the channels are used simultaneously, especially for low crest factor waveforms like sine waves, square waves, and compressed program material.

**Apples vs. Oranges?**

**Amp 1**

_{RMS}for 15 sec into 4 ohms. This amplifier meets the design criteria, and it is only 1 RU and convection cooled. Nice. It’s definitely a contender.

*Figure 4 – Amp 1 I/O matrix. It can hold 24 V*

_{RMS}into 4 ohms for 15 seconds, when driven by 1.3 V_{RMS}.**Amp 2**

_{RMS}for a burst sine is 29 V

_{RMS}, it drops to 18 V

_{RMS}for a continuous sine. This is well below the 22 V

_{RMS}needed to drive the GS to its full acoustic output. The Loading Effect column shows that the amplifier voltage fluctuates wildly under load. This can result in an uneven frequency response, since the load impedance varies with frequency. It’s a 200 W rated amplifier that cannot deliver 121 W for this application. See the problem?

*Figure 5 – Amp 2 I/O matrix. It can hold 18 V*

_{RMS}into 4 ohms for 15 seconds, when driven by 0.8 V_{RMS}.**Amp 3**

_{RMS}into 4 ohms for the continuous sine. It will be coasting at 22 V

_{RMS}. Note that even though it is rated for 2 ohm operation, the V

_{RMS}drops significantly due to the 15 amp limit of the utility power supply. This is to be expected and is mandated by the laws of physics. Utility circuit current is always a consideration with large, multi-channel amplifiers, but one that is obfuscated by typical power ratings which are often based on burst testing alone (the green-shaded area in the matrix).

_{RMS}. That’s about +6 dB higher than Amp 1. While I wouldn’t dare drive the GS with a sine wave at this level, it will provide more peak room for music and speech signals. That’s significant for my application.

_{RMS}into 4 ohms with 12 dB of peak room, all channels driven with about 6 amps of current draw. This will drive the GS to near its thermal limit and make a lot of sound in the space, with only one utility power circuit required.

*Figure 6 – Amp 3 I/O matrix. It can hold 36 V*

_{RMS}into 4 ohms for 15 seconds, when driven by 0.9 V_{RMS}. This is 4.2 dB higher than needed, so reducing the input level by that amount will yield 22 V_{RMS}to the load.**The Decision**

*Photo 2 – The GlobeSource, subwoofer, generator, and amplifier rig. It travels well, rolls well, and produces a LOT of sound.*

**To Summarize**

- The objective is to get the highest possible SPL from a specific loudspeaker.
- Its obscure power and impedance ratings prompted me to measure them for myself.
- This reveal the required amplifier characteristics to drive the load.
- Amplifier ratings don’t usually provide sufficient detail to know the amplifier’s performance under heavy load with sine wave.
- A CAF report does, and producing one gave me the exact information needed.
- I now have every reason to believe that my test rig can achieve the maximum possible SPL from the loudspeaker without damaging it in the process. The result is the best possible signal-to-noise ratio for acoustic testing in large spaces.

**Conclusion**

*pb*