Final answer:
The input voltage needed for three cascaded amplifiers with gains of 20 dB, 26 dB, and 32 dB to get an output voltage of 2V is calculated by first converting the gains to linear values, then multiplying them to find the total gain, and finally dividing the output voltage by the total gain.
Step-by-step explanation:
The student has asked how to calculate the input voltage needed when three amplifiers with voltage gains of 20 dB, 26 dB, and 32 dB are cascaded to produce an output voltage of 2V.
To solve this, we'll need to convert the decibel gains to linear gains using the formula G_linear = 10^(G_dB/20), where G_dB is the gain in decibels. Then, we can multiply the linear gains of all amplifiers together to find the total gain. Finally, we divide the output voltage by the total gain to find the input voltage required.
Gain for 20 dB amplifier: G1 = 10^(20/20) = 10
Gain for 26 dB amplifier: G2 = 10^(26/20) = 19.95
Gain for 32 dB amplifier: G3 = 10^(32/20) = 39.81
Total Gain: G_total = G1 * G2 * G3 = 10 * 19.95 * 39.81
Input Voltage Needed: Vin = Vout / G_total = 2V / (10 * 19.95 * 39.81)
After calculating the total gain and dividing the output voltage by this total gain, the student will arrive at the required input voltage.