The Circuit Designer's Companion - diagramas.diagram...

164 The Circuit Designer’s Companione in = 0R IN−R FR1+e ni n -i n +A V = R F /R INCauseOutput voltage contributionR IN Thermal noise √(4kTR IN ) · A V · √B = N(R IN )R1 Thermal Noise √(4kTR1) · (A V + 1) · √B = N(R1)R F Thermal Noise √(4kTR F ) · √B = N(R F )i n − Amplifier Current Noise i n − · R F · √B = N(i n −)i n + Amplifier Current Noise i n + · R1 · (A V + 1) · √B = N(i n +)e n Amplifier Voltage Noise e n · (A V + 1) · √B = N(e n )Total output noise = √[N(R IN ) 2 + N(R1) 2 + N(R F ) 2 + N(i n −) 2 + N(i n +) 2 + N(e n ) 2 ]Figure 5.15 The op-amp noise modela constant noise spectral density over the bandwidth of interest, which is true forresistors but may not be for the op-amp (see later). Noise, being statistical, is added ona root-mean-square basis. So the general noise model for an op-amp circuit is as shownin Figure 5.15.When the noise is added in rms fashion, if any noise source is less than a third ofanother it can be neglected with an error of less than 5%. This is a useful feature toremember with complex circuits where it is difficult to account accurately for allgenerator resistances.As an example of how to apply the noise model, let us examine the tradeoffs between ahigh-impedance and a low-impedance circuit for different op-amps. The circuit is theR IN−R Fe in = 0R1+standard inverting configuration with R1 sized according to the principle laid out earlier forminimisation of bias current errors (R3 in Figure 5.4). R IN is the sum of generator outputimpedance and amplifier input resistor. The op-amps chosen have the following noisecharacteristics (at 1kHz):OP27: e n = 3nV/√Hz i n = 0.4pA/√Hz (low noise precision bipolar)TL071: e n = 18nV/√Hz i n = 0.01pA/√Hz (low noise biFET)LMV324: e n = 39nV/√Hz i n = 0.21pA/√Hz (industry standard low voltage bipolar)