OP184 Datasheet, PDF (12/20 Pages) Analog Devices – Precision Rail-to-Rail Input & Output Operational Amplifiers

OP184/OP284/OP484
Referring to the op amp noise model circuit configuration illus-
trated in Figure 45, the expression for an amplifier’s total
equivalent input noise voltage for a source resistance level R_S is
given by:
[ ] ^{enT =}
2 (e_nR)² + (i_nOA × R)² + (e_nOA)², units in
V
Hz
where R_S = 2R = Effective, or equivalent, circuit source
resistance,
(e_nOA)² = Op amp equivalent input noise voltage spectral
power (1 Hz BW),
(i_nOA)² = Op amp equivalent input noise current spectral
power (1 Hz BW),
(e_nR)² = Source resistance thermal noise voltage power =
(4kTR),
k = Boltzmann’s constant = 1.38 × 10^–23 J/K, and
T = Ambient temperature of the circuit, in Kelvin, =
273.15 + T_A (°C)
R
e _NR
"NOISELESS"
e _NOA
i _NOA
R
e_NR
"NOISELESS"
i _NOA
IDEAL
NOISELESS
OP AMP
R_S = 2R
Figure 45. Op Amp Noise Circuit Model Used to
Determine Total Circuit Equivalent Input Noise Voltage
and Noise Figure
As a design aid, Figure 46 illustrates the total equivalent input
noise of the OP284 and the total thermal noise of a resistor for
comparison. Note that for source resistance less than 1 kΩ, the
equivalent input noise voltage of the OP284 is dominant.
100
FREQUENCY = 1kHz
T_A = +25°C
OP284 TOTAL
EQUIVALENT NOISE
10
RESISTOR THERMAL
NOISE ONLY
1
100
1k
10k
100k
TOTAL SOURCE RESISTANCE, R_S – Ω
Figure 46. OP284 Total Noise vs. Source Resistance
Since circuit SNR is the critical parameter in the final analysis,
many times the noise behavior of a circuit is expressed in terms
of its noise figure, NF. Noise figure is defined to be the ratio of
a circuit’s output signal-to-noise to its input signal-to-noise. An
expression for a circuit’s NF in dB and in terms of the opera-
tional amplifier's voltage and current noise parameters defined
previously is given by:
NF
(dB )
=
10
log

^{1 +}



(e_nOA)² + (i_nOA
(e_nRS )²
R_S
)²





where NF (dB) = Noise figure of the circuit, expressed in dB,
R_S = Effective, or equivalent, source resistance presented
to amplifier,
(e_nOA)² = OP284 noise voltage spectral power (1 Hz BW),
(i_nOA)² = OP284 noise current spectral power (1 Hz BW),
(e_nRS)² = Source resistance thermal noise voltage power
= (4kTR_S),
Circuit noise figure is straightforward to calculate because the
signal level in the application is not required to determine it.
However, many designers using NF calculations as the basis for
achieving optimum SNR believe that low noise figure is equal to
low total noise. In fact, the opposite is true, as illustrated in
Figure 47. Here, the noise figure of the OP284 is expressed as a
function of the source resistance level. Note that the lowest
noise figure for the OP284 occurs at a source resistance level of
10 kΩ. However, Figure 46 shows that this source resistance
level and the OP284 generate approximately 14 nV/√Hz of total
equivalent circuit noise. Signal levels in the application would
invariably be increased to maximize circuit SNR—not an option
in low voltage, single supply applications.
10
9
FREQUENCY = 1kHz
T_A = +25°C
8
7
6
5
4
3
2
1
0
100
1k
10k
100k
TOTAL SOURCE RESISTANCE, R_S – Ω
Figure 47. OP284 Noise Figure vs. Source Resistance
In single supply applications, it is, therefore, recommended for
optimum circuit SNR to choose an operational amplifier with
the lowest equivalent input noise voltage and to choose source
resistance levels consistent in maintaining low total circuit noise.
–12–
REV. 0