OPA2686 Datasheet, PDF (11/18 Pages) Burr-Brown (TI) – Dual, Wideband, Low Noise, Voltage Feedback OPERATIONAL AMPLIFIER

primary goal, Equation 4 gives a solution for R_F in the input
stage that will provide an equal bandwidth in the first and
second stages, giving the maximum overall channel band-
width.
R_F
=


2
π
Z ^2T
C_D GBP


1
/
3
Eq. 4
Where:
Z_T = Desired total transimpedance gain
C_D = Diode capacitance at reverse bias
GBP = Amplifier Gain Bandwidth Product (MHz)
This equation is used to calculate the required input stage
feedback resistor in Figure 4. The remaining total signal gain
is provided by the second stage; in the example of Figure 4,
setting G = 37.5 gives the same bandwidth (approximately
42MHz) as the bandwidth achieved by the input stage. To
set this first stage bandwidth to its maximally flat values, use
Equation 5 to set the feedback capacitor value:
C_{F =}


π
C_D
R_F GBP


Eq. 5
( ) ( ) ^{f–3dB =}
1
2
(GBP)^{2 / 3}
2 π C_D ^{1/ 3} Z_T ^{1/ 3}
Eq. 6
The approximate achievable bandwidth in the two stages is
given by Equation 6 which gives approximately 30MHz for
Figure 4.
LOW GAIN COMPENSATION FOR IMPROVED SFDR
Where a low gain is desired, and inverting operation is
acceptable, a new external compensation technique may be
used to retain the full slew rate and noise benefits of the
OPA2686 while giving increased loop gain and the associ-
ated improvement in distortion offered by the decompen-
sated architecture. This technique shapes the loop gain for
good stability while giving an easily controlled second-
order low pass frequency response. Considering only the
noise gain (non-inverting signal gain) for the circuit of
Figure 5, the low frequency noise gain, (NG₁) will be set by
+5V
the resistor ratios while the high frequency noise gain (NG₂)
will be set by the capacitor ratios. The capacitor values set
both the transition frequencies and the high frequency noise
gain. If this noise gain, determined by NG₂ = 1+C_S/C_F, is set
to a value greater than the recommended minimum stable
gain for the op amp and the noise gain pole, set by 1/R_FC_F,
is placed correctly, a very well controlled 2nd-order low
pass frequency response will result.
To choose the values for both C_S and C_F, two parameters and
only three equations need to be solved. The first parameter
is the target high frequency noise gain NG₂, which should be
greater than the minimum stable gain for the OPA2686.
Here, a target NG₂ of 10.5 will be used. The second param-
eter is the desired low frequency signal gain, which also sets
the low frequency noise gain NG₁. To simplify this discus-
sion, we will target a maximally flat second-order low pass
Butterworth frequency response (Q = 0.707). The signal
gain of –2 shown in Figure 5 will set the low frequency noise
gain to NG₁ = 1 + R_F/R_G (NG₁= 3 in this example). Then,
using only these two gains and the GBP for the OPA2686
(1600MHz), the key frequency in the compensation can be
determined as:
Z_O
=
GBP
NG₁₂

^{1 –}
NG₁
NG₂


–
1–
2
NG₁
NG ₂



Eq. 7
Physically, this Z₀ (10.6MHz for the values shown above) is
set by 1/(2π • R_F(C_F + C_S)) and is the frequency at which the
rising portion of the noise gain would intersect unity gain if
projected back to 0dB gain. The actual zero in the noise gain
occurs at NG₁ • Z₀ and the pole in the noise gain occurs at
NG₂ • Z₀. Since GBP is expressed in Hz, multiply Z₀ by 2π
and use this to get C_F by solving:
C_F
=
2π
•
1
R _F Z _O NG ₂
(= 2.86pF)
Eq. 8
Finally, since C_S and C_F set the high frequency noise gain,
determine C_S by:
C_S = (NG₂ – 1) C_F (= 27.2pF)
Eq. 9
The resulting closed-loop bandwidth will be approximately
equal to:
f _–3dB ≅ Z_O GBP
(= 130MHz) Eq. 10
1/2
OPA2686
V_O
R_G
250Ω
V_I
C_S
27pF
–5V
R_F
500Ω
C_F
2.9pF
For the values shown in Figure 5, the f_–3dB will be approxi-
mately 130MHz. This is less than that predicted by simply
dividing the GBP product by NG₁. The compensation
network controls the bandwidth to a lower value while
providing the full slew rate at the output and an excep-
tional distortion performance due to increased loop gain at
frequencies below NG₁ • Z₀. The capacitor values shown
in Figure 5 are calculated for NG₁ = 3 and NG₂ = 10.5 with
no adjustment for parasitics.
FIGURE 5. Broadband Low Gain Inverting External
Compensation.
11
®
OPA2686