Question 8.3: Comment on the limitations of Eqs. (8.21) and (8.22) for cal......
Comment on the limitations of Eqs. (8.21) and (8.22) for calculating noise.
V_{o n o i s e,R M S}^{2}=(A_{1} A_{2}A_{3})^{2}V_{i n o i s e,R M S1}^{2}+(A_{2}A_{3})^{2}V_{i n o i s e,R M S2}^{2}+A_{3}^{2}V_{i n o i s e,R M S3}^{2} (8.21)
V_{i n o i s e,R M S}^{2}=V_{i n o i s e,R M S1}^{2}++V_{i n o i s e, R M S2}^{2}/A_{1}^{2}+V_{i n o i s e,R M S3}^{2}/(A_{1}A_{2})^{2} (8.22)
Measured output noise usually includes the thermal noise of the source resistance. If the effective source resistance changes when we cascade the amplifiers, the value calculated for input-referred noise, \textstyle V_{i n o i s e,R M S}, will also change.
A perhaps more important concern is the change in the bandwidth of the noise. Cascading amplifiers results in a reduction in the circuit’s bandwidth. The point of Eqs. (8.21) and (8.22) is still valid, that is, that the first stage’s output noise and gain (equivalent to saying “input-referred noise”) are critical for overall low-noise performance. However, to accurately determine the input-referred noise, it is best to measure the noise on the output of the cascade and then refer it back to the cascade’s input. At the risk of stating the obvious, the gain of the cascaded amplifiers is determined by applying a small sinewave signal to the cascade’s input at a frequency that falls within the amplifier’s passband (not too high or too low). Taking the ratio of the cascade’s output sinewave amplitude to the input sinewave amplitude is the gain. The input-referred noise is then the output RMS noise divided by the gain of the overall cascade.