Bias Card low noise bias lines noise analysis

The low noise detector bias lines in Rev F bias cards are driven by a bipolar DAC (MAX5444AEUB+) whose output is buffered by an opamp (AD797) in a non-inverting configuration (gain G=2), and inverted by a second opamp (AD797). These two signals are then each fed through a series resistance before going to the backplane and MDM connectors. The noise performance of these bias lines is determined by summing the noise contributions of: -the input resistance to the op amp: ~6.3k, mostly due to the output resistance of the DAC -the matched feedback resistances of the buffer, which are internal to the DAC (RFB and INV pins): not listed in the datasheet, but measured as ~12k -the voltage noise of the op amp: 0.9 nV/rtHz at 1kHz -current noise of the op amp: 2.0 pA/rtHz which multiplies both the input resistance to the non-inverting input (~6.3k) and the parallel combination of the feedback resistors at the inverting input (~12k each)

Using these numbers, the total noise at 1 kHz and 300 K can be calculated as:

<math> v_{nt}\ (1kHz,300K) \ = \ G \sqrt { e_n^2 + i_n R_i + i_n (R_{f_1} // R_{f_2}) + 4kTR_i + 4kTR_{f_1}(\frac{R_{f_2}}{R_{f_1} + R_{f_2}})^2 + 4kTR_{f_2} (\frac{R_{f_1}}{R_{f_1} + R_{f_2}})^2 + 4kT} \ \ \ \ \cong \ \ 45 \ \frac{nV}{\sqrt{Hz}} </math>

This characterizes the flat high frequency noise spectrum of the positive polarity bias line before the series resistance. The ~233 ohms of series resistance The ; however, the detector band of interest is up to only 10 Hz. In this band, 1/f noise will be important.