This is a scratch repo for notes and experiments to understand how volume control works on the TLV320DAC3100 I2S DAC used in the Adafruit Fruit Jam board.

Links:

• Datasheet pdf
• Adafruit_TLV320_I2S Arduino library code
• Adafruit_CircuitPython_TLV320 CircuitPython library code (aka adafruit_tlv320)
• adafruit_tlv320 (CircuitPython library) documentation
• Adafruit Forum discussion of Fruit Jam DAC issues

These formulas for power and amplitude dB ratios are from Art of Electronics, third edition, section 1.3.2.

Formula for ratio between the power (Watts) of two signals (P1 and P2) in decibels (dB):

dB = 10 * log10(P2 / P1)

Formula for ratio between the amplitude (Volts) for two signals (A1 and A2) in decibels (dB):

dB = 20 * log10(A2 / A1)

By way of some basic algebra, we can derive a formula to convert dBV to peak voltage (dBV reference value is 1V). Since we're using dBV, we know that A1 is 1V. Also, pow(10, n) is the inverse function of log10(n).

These are the steps to solve the amplitude formula for A2 as a function of dB:

1. dB = 20 * log10(A2 / A1)
2. dB = 20 * log10(A2 / 1)
3. dB = 20 * log10(A2)
4. dB / 20 = log10(A2)
5. pow(10, dB / 20) = A2
6. A2 = pow(10, dB / 20)

For example:

>>> def volts(dBV):
...     return pow(10, dBV / 20)
...
>>> volts(dBV=-10)
0.31622776601683794

The TLV320 has various settings for the voltage level and amplifier gain. I mostly care about the headphone jack, so I need to know what voltage ranges are appropriate for consumer line-level and headphone level output.

1. According to various online sources, consumer line-level is generally about -10dBV, which means 10 dB below a reference voltage of 1 Volt. By calculating pow(10, -10/20), we can see that -10dBV is equivalent to an amplitude of 0.32V.

2. According to this Apple Support page, modern Macs with headphone output jacks adapt to the impedance of connected headphones. For low impedance headphones (under 150 ohms), the output level is up to 1.25V RMS. For high impedance headphones of 150 to 1k ohms, the output level is up to 3V RMS. Generally, cheap headphones are low impedance. Fancy audiophile headphones may be high impedance.