# A front end for wideband A/D converters

Analog-to-digital (A/D) converters are being used to sample increasingly higher frequencies, making the front-end design in a receiver more important than ever. Many applications are moving to super-Nyquist sampling in order to eliminate a mix-down stage, but amplifier performance is limited at these frequencies and their inherent noise will degrade the signal-to-noise ratio. Transformers can be used to replace the amplifier, minimizing noise and providing good coupling at high frequencies, but designing a transformer-coupled front end for wideband A/D converters takes some care.

Transformers' advantages are manifold: They do not pass dc signals and thus provide inherent ac coupling. Making available a noiseless gain that depends on the turns ratio, they also provide an easy single-ended-to-differential conversion. Last, center-tapped transformers provide a single common-mode point, minimizing the components required in the front end.

The impedance ratio is equal to the square of the turns ratio:

Z1/Z2, = a2, where a = N1/N2.

The voltage and current are proportional to the turns ratio:

a = I2/I1 = V1/V2

The transformer gain, in decibels, is 20 log(V2/V1). So, for example, a 1:2 transformer has a gain of 3 dB.

Transformers have many parasitic elements, each of which contributes to frequency response. They exhibit loss, and can be compared to wideband bandpass filters. They also suffer from phase imbalance, with a good transformer having a 1 to 2 percent imbalance across its frequency range.

For example, the interface to the A/D converter can use one or more center-tapped transformers or baluns in various configurations. Each has it advantages and limitations.

With a 2-volt peak-to-peak sine wave applied to the primary, the secondary outputs are each expected to have a 1-V p-p sine wave. This is only partially true, since the phase imbalance will cause a difference between the two secondary outputs. This asymmetry gives rise to even-order distortions on critical analog nodes, which, in turn, leads to second-order harmonic distortion. Using two transformers in series helps to minimize this mismatch. Another way to increase spurious-free dynamic range at high frequencies is to use a two-balun configuration. Acting like transmission lines, baluns usually have more bandwidth than standard transformers and provide good isolation with relatively low loss. The drawback, however, is that they require more power to drive because their input impedance is halved.

An inductor in series with the primary effectively adds a zero to the transfer function, changing the bandwidth of the transformer, increasing the peaking and increasing the variability in required drive power over frequency.

The AD6645 14-bit, 80-Msample/second A/D converter has an input that looks like a 1,000-ohm resistor in parallel with a 1.5-picofarad capacitor. Matching this to a 50-ohm system requires 33-ohm series resistors, used to isolate the A/D converter from the transformer, and shunt resistors of 58 ohms and 501 ohms, as shown (see figure).

(((1000 || 501) + 66) || 58) = 50.65 ohms

In this example, a 1:1 impedance ratio was used, so there is no input voltage gain. This is the easiest type of transformer to configure, but some applications require voltage gain. The parasitics in transformers with other impedance ratios are more difficult to compensate, however, particularly over a wide range of frequencies. In general, the capacitive terms will increase by the square of the turns ratio, while the inductive and resistive terms will decrease by the same factor. The challenge is even more difficult when interfacing with a switched-capacitor A/D converter because the capacitive terms become large and variable over frequency.

*Learn more about transformer front ends for wideband A/D converters in Analog Dialogue (www.analog.com/analogdialogue). *

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Rob Reeder (rob.reeder@analog.com), is an applications engineer at Analog Devices Inc. (Norwood, Mass.)*