Keywords: high-speed comparator jitter
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APPLICATION NOTE 4061

Abstract: In some applications where a high-speed comparator like the MAX999 is used to square an input sinusoidal signal to generate an output clock, it may be important to know the jitter of the generated clock. This application note reviews basic jitter theory and then presents a circuit that can be used to extrapolate the jitter of the MAX999. The jitter measurement is then correlated to the input-referred voltage noise of the comparator.

The summation or convolution of deterministic and random jitter produces

Probability of Data Error (BER) |
Peak-to-Peak (N × RMS) |

10^{-10} |
12.7 × RMS |

10^{-11} |
13.4 × RMS |

10^{-12} |
14.1 × RMS |

10^{-13} |
14.7 × RMS |

10^{-14} |
15.3 × RMS |

The output of the MAX999 has been connected through a 200Ω series resistor and an SMA connector to the Tektronix® CSA8000 communication signal analyzer. The 200Ω series resistor forms a partition with the 50Ω input impedance of the CSA8000 in order to attenuate the input signal at the CSA8000 down to slightly less than 1V

The random jitter of the CSA8000 is specified as 1.0ps RMS (typ) and 1.5ps RMS (max). The HP8082A pulse generator specifies the output jitter to be 0.1% of period + 50ps (peak-to-peak). The output frequency has been chosen to be 80MHz with a 1V

When fed with the input signal described above, the Figure 1 circuit measures an RMS jitter of 11.2ps. Given the simplicity of the circuit, the careful filtering of the power supply, and the low-EMI environment, it is fair to assume that the dominant part of the jitter introduced by the MAX999 and surrounding components is random.

Assuming also that the jitter introduced by the pulse generator and the one introduced by the MAX999 are uncorrelated, it is possible to extrapolate an estimate of the latter's jitter based on the formula in

(RJ_PG)² + (RJ_MAX999)² = (RJ_MEAS)²(Eq. 1)

From this equation, we are able to determine that the MAX999 has a random jitter of 8.1ps RMS.

- The 1ps RMS jitter of the CSA8000 affects the measurement and causes an uncertainty of about 9%.
- It has been assumed that the jitter of the MAX999 is caused only by random jitter related to the thermal noise of the comparator itself and the surrounding resistors. The deterministic jitter is assumed to be very negligible.
- The noise contribution of the two 100Ω resistors that create the 2.5V at the MAX999's negative input is negligible (0.9nV/) and limited in bandwidth by the 7kHz low-pass filter formed with the capacitors in parallel.
- The noise contribution of the 200Ω output series resistor (1.8nV/) may create another source of error because it is not limited in bandwidth. However, as shown in the next section, this contribution is negligible compared to the MAX999's contribution.
- The jitter of the HP8082A pulse generator and the MAX999 have been considered uncorrelated.

Jitter

The HP8082A pulse generator is so limited in bandwidth that the pulses at 80MHz appear as sine waves. For a sine wave, the slew rate in proximity of the zero crossing is given by Equation 3:

SR =

where

V

The contribution of the 200Ω series resistor over the same bandwidth is 14.3µV

¹For a more detailed discussion of jitter, refer to Application Note 1916: