In this application note, we will explain what gain structure is, and how to use this concept to optimize your DSP-based system.
Any component of a hifi system has some fundamental properties, like gain, noise, and maximum signal levels. When multiple components are combined into a system, mismatches in these factors can sometimes lead to unsatisfactory performance, such as excessive noise or signal overload in one or more components.
Noise is present in all electronic systems. You cannot get away from it, but it must be minimized to an acceptable level. In hifi components, the noise level is typically specified as a signal-to-noise ratio (SNR), or how far down the noise is relative to 1 V RMS (typically for line-level components) or full power output (for power amplifiers).
Maximum signal levels
A component has a maximum signal level that it can accept on its input, or generate on its output. In a typical analog line-level component, the output signal is the one to worry about, and is usually determined by the power supply voltage. DSP-based components, however, have very specific maximum input and output levels. In the miniDSP 2x4 kit, for example, the maximum input level can be set by a jumper to either 0.9 V RMS or 2.0 V RMS, and the maximum output level is always 0.9 V RMS.
The gain of a component is the ratio of its output signal level to its input signal level. A preamp with 12 dB of gain, for example, would generate an output signal four times higher than the input signal (with the volume control turned all the way up). A buffer is a special type of component that has 0 dB or unity gain - the output signal is the same as the input signal. A DSP component typically has 0 dB of gain, although some units may vary from this or have switchable input or output levels.
With loudspeakers, we can consider the sensitivity of the speaker (or the drive units, in the case of an active speaker) to be analogous to gain. That is, a speaker with high sensitivity will need less power to produce a desired acoustic output level, which will mean lower signal levels in the electronics components earlier in the chain.
The concept of gain structure is that, at each connection between components in the system, the signal level is as high as it can be (to minimize noise), but no higher than the maximum level that either component allows (so there is no distortion due to overload).
In the diagram below, the dynamic range of a music signal is indicated by a colored rectangle. The signal in red is too high, and will cause distortion. The signal in yellow is too low and the lower signals in the music are below the noise floor. The signal in green is "just right" and represents the ideal music signal level at that connection point. In an optimized system, each interconnection point would be "green" when the volume control is set to the maximum volume that you ever listen to.
It's not generally necessary to compute exactly all of the gains and signal levels throughout a system - understanding the principles of gain structure is usually enough to achieve a good result. The following tips cover the key points for a DSP-based system.
DSP input level
The input signal level to the DSP must never exceed the maximum allowed. If you are connecting a source component such as a DAC directly to a DSP, check the DAC's specifications for maximum output level and ensure that the maximum input level of the DSP is equal to or greater than this. For example, if the DAC max output is 2 V RMS, then you cannot use a 2x4 miniDSP set to 0.9 V maximum input. You must use the 2.0 V setting.
If the DSP is connected to a preamp output, then the 0.9 V input setting is usually preferred, as the signal is already attenuated in the preamp. In most domestic systems, 0.9 V RMS (the maximum DSP output level) will drive the system to high levels, but if higher analog signal levels are needed into the power amps, a unit such as the miniDSP Balanced 2x4 or miniDSP 2x8 kit can be used.
DSP output level
As a general rule, the maximum DSP output level should be equal to or greater than the signal level required to drive your amps to full output power.
However, a problem that occurs in many systems is that the amplifier/speaker combination has too much gain. That is, the maximum output power is never ever used. In this case, the signal level earlier in the chain is pushed down into the "yellow" zone, thus raising the noise present at the speakers. One solution is to reduce the gain of the power amps; another is to place a passive attenuator at the input of the power amps.
Matching levels in an active speaker
In an active speaker, each power amplifier/driver combination needs to be considered. One of the advantages of an active speaker system is that drivers with different sensitivity can be easily used in the same speaker. However, if not done with some care, this can lead to some of the problems noted above. If a loudspeaker driver is much more sensitive than another (for example, you have a 100 dB/W/m horn with an 88 dB/W/m woofer), then you have a mismatch that should be dealt with by reducing the gain of the amplifier on the more sensitive driver. Alternatively, use a passive attenuator at the amplifier input.
This concept of gain structure, taken to its logical conclusion, means that not only are the amplifier gains and corresponding driver sensitivities matched to each other, but the gain of all amplifier/driver combinations is fine-tuned so that the system is capable of producing the maximum output level that you desire, but no more. This ensures minimum noise in the system.
Optimizing the gain structure of your DSP-based system will result in as much SPL as you need, while minimizing noise. A complete analysis of every component is generally not necessary, but keeping in mind some simple guidelines will ensure success.