On Amplifier Gain

We believe good audio should not be a mystery. Building your knowledge of audio fundamentals helps to avoid the common traps of audio foolery.

Amplifier gain remains one of the more common points of confusion, despite the apparent simplicity: press the button and the amp gets louder. Newcomers tend to misunderstand the basics, leading to a myriad of wrong assumptions centered around gain. In this article, we’ll help you to understand the fundamentals of amplifier gain and get the best out of your headphone amp.

What is Gain?

First, it’s important to understand that the voltage applied to your headphones causes the drivers to move. More voltage makes your headphones louder.

Gain is the ratio of the output voltage level to the input voltage level, typically expressed in a unitless form (i.e., 3x), or in decibels (i.e., +9 dB). In simpler terms, gain determines how much amplification is performed. It sets the upper bound for driving your headphones or speakers when the volume knob is at 100%. Mathematically:

$\text{Gain (unitless)} = A_V = \frac{V_{\text{Output}}}{V_{\text{Input}}}$

$\text{Gain (dB)} = A_V = 20 \cdot \log\left(\frac{V_{\text{Output}}}{V_{\text{Input}}}\right)$

The term “gain” in this context refers to Voltage Gain. When voltage output level is the same as voltage input (A_V = 1.0), we refer to this as “unity gain”.

Gain vs. Volume

Gain is the amount of amplification applied to the input signal, whereas you set the final output level delivered to your headphones using the volume control. Put another way, appropriate gain is what enables you to reach a high output volume.

Why Gain Matters

Setting the proper gain level is crucial for optimizing the noise floor or reaching extreme listening volumes. Too much gain can lead to excessive noise, while too little gain can result in insufficient volume, as we’ll explain in more detail below.

The Role of Source Signal Level

One common reason to invest in an amplifier is to overcome weak volume. Keep in mind that headphone amps built within the past decade are generally designed to be paired with 2 V_RMS DACs. If you feed your amplifier with a weaker audio signal, you may not be as impressed as you hoped!

Maximum Amplifier Output

Let’s rearrange the gain equation:

V_max-output = Gain × V_Input

Put simply, your amplifier’s max output volume is directly proportional to the audio source feeding your amp, via gain. For example, if an amplifier has a gain of 4.5x and the input signal is 2 V_RMS, its theoretical max output voltage would be:

V_max-output= 4.5 × 2 V_RMS = 9 V_RMS

If you connect the same amplifier to a typical laptop or smartphone providing only 1 V_RMS, max output is then limited by 50%:

V_max-output= 4.5 × 1 V_RMS = 4.5 V_RMS

Gain Determines Power

Power is defined as:

P = VI

We can use Ohm’s law to see that Power depends on listening volume (V_output), for a given headphone impedance (R):

$\text{Power} = \frac{(V_{\text{Output}})^2}{R}$

And substituting in the Max Amplifier Output equation, we arrive at:

$\text{Power} = \frac{(\text{Gain} \times V_{\text{Input}})^2}{R}$

In other words, achieving peak volume from your headphones depends on providing an appropriate audio signal to your amp (V_in) at appropriate Gain.

Note the Limits

Also keep in mind the Max Amplifier Output and Power equations presented above are simplified to a purely resistive model, and assume all other constraints placed on the amplifier are satisfied. An amplifier can only amplify so much before it reaches its internal limits (power supply voltage or current limits, thermal limits, IC current limits, load impedance interactions, etc.). Distortion or clipping becomes obvious when an amplifier is pushed beyond its capabilities.

Max output may vary with headphone impedance, so it’s useful to review an amp’s output rating specs not just in terms of power, but in terms of V_output. When an amplifier’s current (I) supply is abundant, its Power vs. Resistance curve will appear linear on a logarithmic scale. Conversely, if output current is limited by the amplifier’s design, the Power curve will appear non-linear. For example, the difference between a 1W Atom Amp+ and a 2.6W Atom Amp 2 is due to a large increase in I, and a small increase in Voltage Gain:

$P = \frac{I \times (\text{Gain} \times V_{\text{in}})^2}{V_{\text{out}}}$

It’s further worth noting that an “increase in I” implies Current Gain. We’ll save this discussion for another time.

Avoiding Excess Gain

It’s best to use the lowest gain necessary to reach your desired listening level. Since gain amplifies the input signal, any background noise present from the source is also amplified. Of course, modern DACs perform exceptionally well, making source noise rarely audible even with high sensitivity IEMs. For a deep dive on excess gain, check out NwAvGuy’s article, “All About Gain”.

By the way, Element III manages gain automatically, so that you’re always listening in the optimal state.

Designing Gain and Input Sensitivity

Smaller source levels of 0.5-1 V_RMS were typical in the early 2000s and we spent years building amplifiers with custom gain to match customers’ setups. By the mid 2010s, most of our customers began listening to DACs with 2 V_RMS outputs. This level has become the de facto standard for headphone amps.

Thus, we design all JDS Labs amplifiers to continuously run free of clipping when paired with matching 2 V_RMS DACs unbalanced, or 4 V_RMS balanced.

Gain is the last choice in our amplifier designs. We first push new amplifiers to their limit via audio analyzer under several dummy loads. By observing an amp’s max V_Output under an input sensitivity of V_Input= 2 V_RMS, gain is then a basic design calculation.

Not all amps are designed this way! Gain can be set way beyond the capability of an amp, or a high level may be intended to reach extra volume from low recordings. For more detail on this topic, see Power is Volume.

Yes, we can still customize the gain of amplifiers like Atom Amp 2. If you happen to have a weak phono preamp, or a strong interface that delivers nowhere near 2 V_RMS, let us know. This may delay your order by a few days, but a custom gain level is key if not using a DAC.

Volume Knob Position

Your amp’s volume knob position is not a reliable indicator of power or gain! Comparing the knob position between brands and models of amplifiers is a fairly meaningless task. The choice of potentiometer taper or use of an encoder determines how aggressive the knob will be, and position markings can be rather arbitrary.

Our analog amplifiers use 15A style tapers to achieve gradual volume adjustment. Strive to set your source and gain so that the volume knob lands between 10-2 o’clock. In general, if the knob is near its minimum position, gain may be too high or the audio source volume may need to be reduced to better suit your headphones. Conversely, it’s perfectly safe to listen to your JDS Labs amplifier with its knob at 100%. While high volume is unsafe for your ears, our amps are designed to handle a full load.

Practical Considerations

When setting up your audio system, consider the entire signal chain. In rough order of importance:

Source Signal Level: Ensure that your audio source provides a 2 V_RMS signal, such as any JDS Labs DAC. For reference:
- PCs and laptops: Typically 1 V_RMS, although some are stronger or weaker
- Smartphone 3.5mm dongles: 0.5-1 V_RMS
- Newer Macs: Up to 3 V_RMS
- Interfaces: Anywhere from 1-7 V_RMS
- Phono preamps: Typically 150mV = 0.15 V_RMS
Amplifier Gain: Set gain to the lowest position. Switch to high gain only when you need more volume.
Music/Recording Level: Different recordings have varying levels of signal intensity. Raise volume and gain as needed.
Volume Knob Position: Not critical!

Conclusion

Understanding gain and its impact on your audio setup is key to unlocking the full potential of your headphone amp. In short, if you wish to achieve max volume, pair your JDS Labs amp with its matching DAC. As always, feel free to reach out if you have any questions!