Question 6.5: For a compressor with a μ = 255, determine a. The voltage ga......
For a compressor with a μ = 255, determine
a. The voltage gain for the following relative values of V_{in}: V_{max}, 0.75 V_{max}, 0.5 V_{max}, and 0.25 V_{max}.
b. The compressed output voltage for a maximum input voltage of 4 V.
c. Input and output dynamic ranges and compression.
a. Substituting into Equation 10, the following voltage gains are achieved for the given input magnitudes:
V_{out}=\frac{V_{max}\,ln(1\,+\, μV_{in}/V_{max})}{ln(1\,+\, μ)} (10)
table 1
b. Using the compressed voltage gains determined in step (a), the output voltage is simply the input voltage times the compression gain:
Table 2
c. Dynamic range is calculated by substituting into Equation 4:
DR = 20 \log\,\frac{V_{max}}{V_{min}} (4)
input dynamic range = 20 \log\frac{4}{1} = 12 dB
input dynamic range = 20 \log\frac{4}{3} = 2.5 dB
compression = input dynamic range minus output dynamic range
= 12 dB − 2.5 dB = 9.5 dB
To restore the signals to their original proportions in the receiver, the compressed voltages are expanded by passing them through an amplifier with gain characteristics that are the complement of those in the compressor. For the values given in Example 5, the voltage gains in the receiver are as follows:
Table 3
The overall circuit gain is simply the product of the compression and expansion factors, which equals one for all input voltage levels. For the values given in Example 5,
V_{in} = V_{max} 1 × 1 = 1
V_{in} = 0.75 V_{max} 1.26 × 0.79 ≅ 1
V_{in} = 0.5 V_{max} 1.75 × 0.57 ≅ 1
V_{in} = 0.25 V_{max} 3 × 0.33 ≅ 1
Table 1
| V_{in} | Compressed Voltage Gain |
| V_{max} | 1.00 |
| 0.75 V_{max} | 1.26 |
| 0.5 V_{max} | 1.75 |
| 0.25 V_{max} | 3.00 |
Table 2
| V_{in} | Voltage Gain | V_{out} |
| V_{max} = 4 V | 1.00 | 4.00 V |
| 0.75 V_{max} = 3 V | 1.26 | 3.78 V |
| 0.50 V_{max} = 2 V | 1.75 | 3.50 V |
| 0.25 V_{max} = 1 V | 3.00 | 3.00 V |
Table 3
| V_{in} | Expanded Voltage Gain |
| V_{max} | 1.00 |
| 0.75 V_{max} | 0.79 |
| 0.5 V_{max} | 0.57 |
| 0.25 V_{max} | 0.33 |