# Accurately predict measured noise figures for transformer coupled differential amplifiers (Part 2 of 2)

Using a transformer-coupled differential inverting amplifier stage can give a very low input referred noise voltage or Noise Figure (NF) with exceptional SFDR/mW of power. Modern FDA’s can deliver below 7dB noise figures using this approach with intended signal frequencies from 100 kHz to >500 MHz. Part 1 showed the theoretical expression including the transformer insertion loss. This accounted for some of the higher measured NF vs. theoretical getting to within 0.4dB of bench.

Part 2 continues this sweeping the target total gain while stepping up the turns ratio using the ISL55210, then shows a 1:2 turns ratio selection and compares predicted noise figures and closed loop bandwidths over a wide gain range using the best FDA’s available. Using those same FDA’s, an estimate of closed loop bandwidth is generated with and then also without the transformer bandwidth included.

**Example swept gain designs using low insertion loss transformers and the ISL55210**

Having the more accurate noise figure expression in eq. 3 (repeated here), select a range of turns ratio transformers having low insertion losses and generate the expected noise figure over a swept total gain using those transformers and the very low noise ISL55210. The selected transformers are shown in Table 3 with their necessary parameters.

**Equation 3**

**Table 3. Stepped turns ratio transformers shown for design examples. **

These example transformers are a small subset of a large range of available wideband transformers. While these are specified as 50Ω, that is simply the characterization impedance for showing the frequency response. Transformers are very flexible on source and load impedances where changing those simply shifts the passband frequency response (ref.4).

Using the 4 transformers in Table 3, generate the expected noise figure over target total gains from 12dB to 32dB (4V/V to 40V/V). This is simply setting the R_{g} elements in figure 1 to get the match then stepping the R_{f} resistors to get the desired gains including the transformer insertion loss effects. That initial setting for the 1:2 turns ratio case (starting gain of 12dB) is shown in Table 4.

**Table 4. Initial setup for Noise Figure sweep using the ADT4-6T transformer.**

Note the initial R_{f} value is slightly over 200Ω to account for this transformers’ insertion loss. Running 4 sweeps with the different transformers of Table 3 gives a more accurate estimate of NF in figure 4.

**Figure 4. Predicted NF is graphed over gain for 4 different low insertion loss transformers with ISL55210**

One of the interesting results of figure 4 is the relatively slight difference in the first 3 turns ratios in the resulting noise figure. As the turns ratio goes up, the voltage noise term goes down while the current noise term goes up. But, since lower amplifier gains are also required to hit the same total gain, the α in equation 2 is also going down actually increasing some of the noise terms giving the almost constant profile over total gain of figure 4.

At the highest turns ratio of 1:3, a definite degradation is seen. Here, the resistor values have been scaled up so much to render the FDA input current noise contribution (5pA for the ISL55210) in equation 3 dominant. The important result of Figure 4 is to suggest using the turns ratio of 2 if the desired transformer supports the intended frequency band. At any given gain, the NF is very similar to using lower turns ratios but since the voltage feedback FDA will be operating at lower gain, it will be providing more bandwidth and loop gain vs. the designs using lower turns ratios and hitting the same total gain. This should move in the direction of improved harmonic distortion.

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