Designing For High Speed In Current-To-Voltage Conversion

May 8, 2008
As new communications systems reduce the number of RF up-conversions, design of the digital-to-analog stage becomes more challenging.

Communications channels used to be a challenging exercise in pure analog design. Today, modulation occurs in the digital domain in many systems. But the transmitted signal is analog, so there’s always a conversion.

For any communications system, choices for the digital- to-analog converter (DAC) and its current-to-voltageconverting op amp depend on the required bandwidth. As DACs and op amps get faster, they move closer to the transmitting antenna.

The DAC needs to convert digital inputs and settle fast enough to reproduce the modulated signal. The simplest option for converting a DAC’s current output to voltage is to use a single-ended transimpedance circuit. It avoids DAC compliance problems and gives low distortion.

However, the op amp used for the transimpedance amplifier needs to slew fast enough to match the DAC’s output, sink or source its full-scale current, and drive the load. Additionally, transimpedance compensation must keep bandwidth wide enough without excessive peaking or oscillation.

A differential current-to-voltage circuit may provide wider bandwidth, at the expense of higher noise and distortion. With the right design choices for the application, highfrequency operation is definitely within reach.

For applications like video, the analog circuit needs to drive a terminated coaxial or unshielded twisted-pair cable. In others, the analog signal drives other circuits. The difference is in the load. Doubly terminated coax will present 37.5 O or 25 O. Doubly terminated, category 5, unshielded twisted pair gives a balanced 50 O. Another circuit may be 1k or more, but lower impedances deliver higher speed.

BANDWIDTH AND SPEED What frequency range is important? That depends on the carrier and modulation frequencies. Many RF receivers and some transmitters need a tightly controlled sinusoidal source of 10.7 MHz. Scrambled 100BaseTX Ethernet produces important frequencies starting around 10 MHz, with signal components extending to 120 MHz. Five-level signaling of 1000BaseT gives a similar spectrum on each of the four twisted pairs it uses.

Necessary slew rate depends on the highest baseband frequency and amplitude to be reproduced by the analog output. For a 100BaseTX MLT-3 transmitted signal within the specified template, 300 V/µs between 0 and +1 V and 0 and –1 V would do it. For a 10.7-MHz, 2-V sinusoid, the maximum slew rate is sine_SR(f) := 2pVP, 134 V/µs.

Assuming a DAC conversion rate more than twice the Nyquist frequency, DAC settling time determines the upper limit of the DAC’s output frequency range. Op-amp settling time to 1 LSB also shows an upper bound on output frequency for an accuracy level.

Op-amp settling times are usually specified from a large input step to 0.1%, 0.01%, and, rarely, 0.001% at noninverting unity gain. These percentages correspond roughly to 10-, 13-, and 16-bit LSBs. Performance to unspecified levels at different gains may be approximated from typical performance graphs, but there’s no substitute for testing on the bench once an initial choice is made.

SPECTRAL PURITY, NOISE, AND RESOLUTION Next, consider harmonic distortion, which can be specified in several ways. The most common for op amps are second- and third-harmonic levels below fundamental, expressed as dBc (dB below carrier). Second and third harmonics are used because they’re usually the largest.

DAC distortion is also specified a number of different ways. The most useful for an application with a large frequency range is spurious-free dynamic range (SFDR) to Nyquist. This is the ratio of rms signal to rms peak spurious spectral content up to the Nyquist frequency. SFDR specified in a frequency band is more important to synthesizing a strong single tone for a narrowband transmitter.

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SFDR to Nyquist offers a glimpse of what to expect for DAC noise. However, only a signal-to-noise plus distortion (SINAD) specification gives the entire story.

Op-amp noise specifications appear as voltage and current noise densities at a particular frequency. Many op amps might seem to give low enough noise levels to be ignored, but it pays to check for the application’s frequency band. In RF applications, the op amp’s 1/f or other low-frequency noise usually isn’t a factor.

Output voltage is deceptively simple. A standard may specify a tight range for the output swing, or you may know the precise level you need to drive something else. Getting the circuit to that level requires a few more answers. What’s the DAC’s full-scale output current for acceptable harmonic distortion? What output load is the op amp driving? Can the op amp drive the right level at the required frequencies and distortion?

Finally, there’s DAC resolution. Quantization error translates into signal-to-distortion ratio for a full-scale sinusoid relatively easily. More resolution will be needed if the output level covers a wide range. The application may have a target SINAD ratio for the low end of the output range plus a maximum level to drive. You’ll need enough resolution for the low end’s SINAD requirement, plus enough additional bits to reproduce the maximum level.

DIFFERENTIAL OR SINGLE-ENDED CONVERSION? The first design choice for a current-output DAC is differential versus single-ended voltage conversion. Preserving differential output with a well-balanced load provides low commonmode distortion and noise rejection. The simplest differential solution is a center-tapped transformer.

In most systems driving a terminated transmission line, a DAC termination resistor will also be necessary. If complex filtering is to be performed on the DAC’s output, driving a transformer directly may not be the best choice.

A dual-supply op amp is a better differential choice when the DAC’s output will be filtered or undergoes further analog processing, or if dc response is needed. In Figure 1, each DAC output drives a 25-O load with 20 mA full-scale. This creates out-of-phase output voltages of 0 to 0.5 V. The op-amp circuit has a gain of one to create a 1-V p-p output.

C1 forms a differential filter with the equivalent 50-O DAC output load. This filter reduces any slew-induced distortion from the op amp, if necessary. This circuit’s high commonmode rejection provides good common-mode noise immunity and cancels some of the even harmonic distortion. Commonmode rejection depends on resistor matching, so 0.1% resistors or better should be used.

The differential op-amp circuit does have some disadvantages. DAC nonlinearity can be affected by voltage-compliance limits at full-scale outputs. Op-amp bandwidth will decrease with gain and higher gain-setting resistor values, meaning more noise.

Op-amp slew rate at the gain used must be fast enough to follow the DAC output. To reproduce a 100BaseTX output signal at full amplitude, the op amp needs to slew at least 300 V/µs. If it can’t, slew distortion will slow waveform edges and generate code-dependent jitter in the output. Edge distortion also results when C1 is used to slow down DAC output so the op amp can follow it.

SINGLE-ENDED SIMPLICITY A single-ended current-to-voltage conversion delivers the best DAC nonlinearity, since the DAC drives a virtual ground. The transimpedance circuit shown in Figure 2 develops a –1-V output across RF from the DAC’s 10-mA full-scale output.

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Figure 2’s transimpedance circuit is unstable without capacitor CF to roll off the noise gain. Without CF, the DAC’s output capacitance and the op amp’s input capacitance create a zero, and noise gain increases indefinitely at 6 dB per octave, causing instability. If RS is the paralleled resistances at the transimpedance-amplifier input and CS is total input capacitance (the sum of DAC output and transimpedance-amp input capacitances), the transimpedance amplifier’s noise gain is:


guarantees stability, at the expense of bandwidth. The value that produces CF with 45 degrees of phase margin is:

This CF value starts to flatten noise gain before it intersects the op amp’s open-loop gain curve. To maintain stability, the slope difference between the two curves should be less than 12 dB/octave at the point of intersection.

A DESIGN EXAMPLE Let’s look at a high-bandwidth design. For an op amp such as Analog Devices’ ADA4899-1, typical differential RIN is 4k, and –3-dB bandwidth is 600 MHz at unity gain. A DAC like Analog Devices’ AD9755 has typical COUTDAC = 5 pF and ROUTDAC = 100k. DAC output capacitance and resistance are both code-dependent, but the typical values can be used to get a starting value for CF.

The DAC specifies a 300-Msample/s update rate and 61-dBc SFDR to Nyquist at 101.1-MHz output. If input data changes at least 2 ns before or after clock rising edges, the DAC shows a 63-dBc signal-to-noise ratio. SINAD is about 62 dB at 300 Msamples/s and 10 MHz, so the effective number of bits is 10 for those conditions.

The op amp can drive a 100-O load to over ±3 V. For a -1-V full-scale output voltage, use a 10-mA full-scale output current from the DAC and RF = 100 O. The op amp needs to sink the DAC’s full-scale current and the load current, so 50 O from the combination of RF and the voltage output load shouldn’t be a problem for a –1-V output swing.

Also, the op amp has a 120-MHz, –3-dB bandwidth for 1-V output across a 100-O load. Using Equation 3 with these component values, CF = 11.2 pF. This should be a surfacemount capacitor with low effective series inductance and resistance.

The transimpedance amplifier’s 3-dB output corner frequency is approximately:

For the example, this gives 69 MHz. But this CF value is only a starting point. Breadboarding the circuit and checking stability with real components is necessary to produce a working design. (More often than not, CF is determined empirically.)

The differential conversion offers more bandwidth. ROA-B in parallel with the DAC output capacitance and R1A-B in series with the op-amp inputs keep the noise gain reasonably flat for stability without extra compensation capacitors. Figure 3 shows the input and output capacitances and resistances between the DAC and op amp in the differential circuit.

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For a 1-V output, choose 20 mA full-scale from the DAC. Configure the op amp for unity gain with the values in Figure 1. Not all high-frequency op amps are unity-gain-stable, which is important for highest bandwidth in a differential application. The ADA4899-1’s unity-gain –3-dB bandwidth is about 120 MHz for a 1-V output.

Using the lower half of Figure 3’s circuit with C1 = 0 gives a pi-section filter with a low-pass voltage transfer function. The approximate –3-dB rolloff point is 123 MHz, so the op amp sets the response limit in this example. Op-amp settling time may set a lower limit to maintain required harmonic levels.

The op amp and its resistors contribute noise to the output in both circuits. The op amp’s input-referred voltage noise density VN is 1 nV/vHz. Its input-referred current noise density IN is 2.6 pA/vHz. Each circuit has three noise contributors: voltage noise from the op amp, voltage noise from op-amp noise current through the resistors, and the resistors’ thermal noise.

In the equations below, ROUTDAC is DAC output resistance, RIN_DIFF is op-amp input resistance, COUTDAC is DAC output capacitance, and CIN is op-amp input resistance. For the transimpedance circuit, noise gain GN varies with frequency:

Thermal noise per root hertz from RF at the output is:

Output voltage noise density from just the op amp is:

Output noise density from noise current through RF is:

The transimpedance amp’s total output noise density is:

At 100 kHz, total output noise density is 1.75 nV/vHz. For the 100-MHz band above 100 kHz, total output noise is 17.5 µV. For comparison, a 14-bit LSB for 1-V full-scale is 61 µV.

DIFFERENTIAL VOLTAGE CONVERTER NOISE The differential circuit has more output noise. Noise gain GN is a constant 1.91. It’s lower than the expected 2 due to ROB. For noise analysis, treat the sums RINA = R1A + ROA and RINB = R1B + ROB as single resistors.

For each resistor, input-referred thermal noise density is:

Output voltage noise density from just the op amp is VNamp = VN × GN. Output noise density from noise current through each resistor combination is:

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Output thermal noise density is different for each resistor. For R2A, it is:

For RINA, it is:

For R1B:

For R2B:

The total output noise density is:

The differential circuit’s output noise density is 4.8 nV/vHz. Total voltage noise for the 100-MHz band above 100 kHz is 47.7 µV, over half a 14-bit LSB. In some applications, with the DAC’s ENOB of 10, the op-amp noise may not be significant. But it needs to be RMS-averaged with other noise sources for the full picture.

This simple analysis considered a few of the factors in choosing circuits for the voltage output in a high-frequency communications system with digital synthesis and showed what was possible with a fast, low-noise op amp. Multitone communication systems will place higher demands on the DAC and op amp. But any system needs to be built and characterized in conditions similar to those in the final application to guarantee wideband performance.

JOHN ARDIZZONI, application engineer in Analog Devices’ High Speed Amplifier Group, has authored numerous papers and is a contributing writer for the company’s RAQ’s column. He received his BSEE from Merrimack College, North Andover, Mass. He can be reached at [email protected].


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