To determine the voltage gain, compressed output voltage, and input/output dynamic ranges for a compressor with a μ of 255, we can use the following formulas:
(a) Voltage gain (VG) is given by:
\[VG = \frac{1}{\mu} = \frac{1}{255}\]
(b) Compressed output voltage (Vout) for a maximum input voltage of 4V is:
\[Vout = Vin^{VG} = 4^{1/255}\]
(c) Input and output dynamic ranges for different relative input values can be calculated by using the formula:
\[Dynamic Range = 20 \cdot \log_{10}(V_{max}/V_{min})\]
Let's calculate the values:
(a) Voltage gain:
\[VG = \frac{1}{255} \approx 0.00392\]
(b) Compressed output voltage for a maximum input voltage of 4V:
\[Vout = 4^{1/255} \approx 1.043\]
(c) Input and output dynamic ranges:
- For \(V_{max}\):
\[Dynamic Range = 20 \cdot \log_{10}(4/0) = \infty\]
- For \(0.75V_{max}\):
\[Dynamic Range = 20 \cdot \log_{10}(3/0.75) \approx 12.04\,dB\]
- For \(0.5V_{max}\):
\[Dynamic Range = 20 \cdot \log_{10}(2/0.5) = 12.04\,dB\]
- For \(0.25V_{max}\):
\[Dynamic Range = 20 \cdot \log_{10}(1/0.25) = 12.04\,dB\]
These are the values for the voltage gain, compressed output voltage, and input/output dynamic ranges for the given compressor with a μ of 255.
PH