# Considering only the noise gain this is the same as

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Considering only the noise gain (this is the same as the non- inverting signal gain) for the circuit of Figure 4, the low frequency noise gain, (NG 1 ) will be set by the resistor ratios while the high frequency noise gain (NG 2 ) will be set by the capacitor ratios. The capacitor values set both the transition frequencies and the high frequency noise gain. If the high frequency noise gain, determined by NG 2 = 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 F C F , is placed correctly, a very well-controlled, second-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 NG 2 , which should be greater than the minimum stable gain for the OPA687. Here, a target NG 2 of 24 will be used. The second parameter is the desired low frequency signal gain, which also sets the low frequency noise gain NG 1 . To simplify this discussion, we will target a maximally flat second-order low pass Butterworth frequency response (Q = 0.707). The signal gain of –4.25 shown in Figure 4 will set the low frequency noise gain to NG 1 = 1 + R F /R G (= 5.25 in this example). Then, using only these two gains and the GBP for the OPA687 (3600MHz), the key frequency in the compensation can be determined as: Z O = GBP NG 1 2 1 – NG 1 NG 2 1 – 2 NG 1 NG 2 C F = 1 • R F Z O NG 2 C S = NG 2 –1 ( ) C F f 3 dB Z O GBP Physically, this Z 0 (4.1MHz for the values shown above) is set by 1/(2 π • 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 NG 1 • Z 0 and the pole in the noise gain occurs at NG 2 • Z 0 . Since GBP is expressed in Hz, multiply Z 0 by 2 π and use this to get C F by solving: Finally, since C S and C F set the high frequency noise gain, determine C S by [Using NG 2 = 24]: The resulting closed-loop bandwidth will be approximately equal to: For the values shown in Figure 4, the f –3dB will be approxi- mately 121MHz. This is less than that predicted by simply dividing the GBP product by NG 1 . 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 NG 1 • Z 0 . The capacitor values shown in Figure 4 are calculated for NG 1 = 5.25 and NG 2 = 24 with no adjustment for parasitics. The full circuit on the front page of this data sheet shows the capacitors adjusted for parasitics. The front page of this data sheet shows the measured 2-tone, 3rd-order distortion for just the amplifier portion of the circuit.

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