Prototype System
Chapter 11 Results
11.3 Noise Performance
(a) (b)
Figure 11.10: Measured results at 2.5 Mbit/s data rate with zero open loop gain error: (a) eye diagram, (b) output spectrum (1.84 GHz center frequency, 10 MHz span).
Figure 11.11 shows measured eye diagrams from the prototype at three open loop gain settings and two different data rates. The measured results shown in Figure 11.11 are nearly identical to those obtained from simulation.
11.3 Noise Performance
The noise performance of the transmitter is evaluated in this section. We begin by showing simulated spectra of the transmitter in its unmodulated state, and then use simulations to examine the impact of modulation on the output spectrum. Measured results are then presented and compared to simulations.
11.3.1 Noise Measurement Considerations
We seek an overall noise specification at the transmitter output that is less than -131 dBc/Hz at 5 MHz offset from the carrier when the data rate is set to 1.25 Mbit/s.
Measurement of this low noise value is problematic with spectrum analyzers due to their limited dynamic range. To mitigate this problem, all noise measurements were taken with an HP 3048A phase noise measurement system that was used in conjunction with the frequency discriminator method. Unfortunately, the dynamic range of this instrument is insufficient to measure phase noise at the desired levels while the transmitter is modulated. (The energy of the phase transitions is greatly
(a) (b) (c)
(d) (e) (f)
Figure 11.11: Measured eye diagrams at 1.25 Mbit/s and 2.5 Mbit/s for three different open loop gain settings: (d) 1.25 Mbit/s, -25% gain error, (e) 1.25 Mbit/s, 0% gain error, (f) 1.25 Mbit/s, 25% gain error, (a) 2.5 Mbit/s, -25% gain error, (b) 2.5 Mbit/s, 0% gain error, (c) 2.5 Mbit/s, 25% gain error.
increased during modulation, which forces the HP 3048A to bypass its LNA and thereby increase its noise floor.)
To overcome this obstacle, the transmitter’s modulated noise performance will be inferred from measured phase noise data taken from the transmitter in its unmodu-lated state. Specifically, it will be assumed that at an offset frequency of 5 MHz and a data rate of 1.25 Mbit/s, the modulated transmitter output spectrum, Sout(f ), has the same spectral density as its unmodulated phase noise spectrum, SΦtn(f ). We will present simulated results that confirm that this is a reasonable assumption.
When measuring the phase noise of the transmitter in its unmodulated state, the digital data path is exercised with a periodic dithering sequence applied to the least significant bit of its modulation bus. Application of the dithering sequence avoids the generation of spurious noise in the Σ-∆ modulator, and is used when obtaining both simulated and measured phase noise spectra when the Σ-∆ is included. Figure 11.12 displays one period of the dithering sequence that was used, along with its power spectrum. The sequence was generated by sending half a cycle of a digitized sine
11.3. NOISE PERFORMANCE 175
waveform into the input of a first order, MASH Σ-∆ modulator. A relatively flat spectrum was achieved for the sequence by a trial-and-error procedure; namely, the amplitude of the input sine wave was reduced until acceptable results were obtained.
The resulting spectrum in Figure 11.12 is seen to have a periodic bumpiness. Fortu-nately, this bumpiness has negligible impact on the transmitter output spectrum; an explanation its occurrence was not determined. Note that one period of the sequence is 32K samples long, which translates to a fundamental frequency of 610 Hz since the data is fed in at 20 MHz.
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Power Spectrum of Dithering Sequence (20 MHz sample rate assumed)
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Figure 11.12: Binary dithering sequence fed into least significant bit of digital modulation path.
11.3.2 Simulated Results
The simulation model of the transmitter in this section includes the noise sources Isum(t) and Vsum(t) described in the Chapter 10 so that an accurate representation of SΦtn(f ) is achieved. A model for the switched capacitor loop filter that is used in the prototype is also included; this filter is operated under Case 1 conditions, as defined in Chapter 9.
Figure 11.13 shows the simulated output phase noise, SΦtn(f ), of the unmodulated transmitter with the Σ-∆ removed and in place. These spectra agree well with the calculated noise spectrum displayed in Figure 10.8 of Chapter 10. (Note that I was set to 1.5 uA in the simulations.) The simulated spectra include the spurious tone that is present at 20 MHz due to the fifty percent nominal duty cycle of the PFD output. A bumpiness is seen in the simulated spectra at frequencies between 1 and 10 MHz; this phenomenon is an artifact of the decreased number of sample points used to compute the spectrum at lower frequencies, and imperfections in the numerical
procedure used to generate the charge pump noise (i.e., the sequences do not have a perfectly flat spectrum). Simulated data at frequencies lower than 100 kHz is not shown due to the small number of data points calculated for this region.
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Simulated Synthesizer Phase Noise (Sigma−Delta removed)
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Simulated Synthesizer Phase Noise
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Figure 11.13: Simulated phase noise, SΦtn(f ), of unmodulated synthesizer: (a) Σ-∆
removed, (b) Σ-∆ in place and appropriately dithered.
Comparison of Figure 11.13(a) to Figure 11.13(b) reveals that Σ-∆ quantization noise has the dominant influence on phase noise performance at intermediate frequen-cies. With the Σ-∆ included, the phase noise density at 5 MHz offset frequency is -132 dBc/Hz.
The influence of modulation on the output spectrum is seen in Figure 11.14, which displays plots of Sout(f ) and SΦout(f ) at two different data rates. (Sout(f ) is the power spectral density of the transmitter output, while SΦout(f ) is the power spectral density of the instantaneous phase of the transmitter output. See Chapter 3 for details.) At 1.25 Mbit/s, we see that Sout(f ) ≈ SΦtn(f ) for frequencies in the range of 5 MHz; this confirms that measurements of SΦtn(f ) can be used to evaluate the noise performance of the modulated transmitter at this frequency offset. At 2.5 Mbit/s, the output spectral density is raised to -130 dBc/Hz at 5 MHz offset due to the higher bandwidth of the modulation signal.
A few artifacts appear in SΦout(f ) that deserve explanation. First, spurious tones are seen at multiples of the data rate; these tones are an artifact of modulating the duty cycle of the PFD output, as discussed in Chapter 9. Fortunately, the spurs do not show up in the output spectrum, Sout(f ), since they are convolved with the modulation spectrum. Second, each plot of SΦout(f ) contains bumps at 20 MHz;
their appearance is a direct consequence of compensating the discrete-time signals used to create Φmod(t), as will now be explained. Using notation from Chapter 5, compensation of insd(t) causes its spectral density, Sinsd(f ), to rise dramatically at
11.3. NOISE PERFORMANCE 177
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Simulated Phase Noise of Modulated Synthesizer at 1.25 Mbit/s
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Simulated Output Spectrum of Modulated Synthesizer at 1.25 Mbit/s
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Simulated Phase Noise of Modulated Synthesizer at 2.5 Mbit/s
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Simulated Output Spectrum of Modulated Synthesizer at 2.5 Mbit/s
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(c) (d)
Figure 11.14: Simulation results of PLL output spectrum with noise sources in-cluded: (a) SΦout(f ) at 1.25 Mbit/s, (b) Sout(f ) at 1.25 Mbit/s, (c) (a) SΦout(f ) at 2.5 Mbit/s, (d) Sout(f ) at 2.5 Mbit/s.
frequencies higher than fo until the bandwidth of W (f ), B, is reached. At frequencies higher than B, Sinsd(f ) falls sharply due to attenuation imposed by W (f ). Since insd(t) is effectively sampled at rate 1/T = 20 MHz, a replica of its spectrum is seen at 20 MHz; the relatively low DC value of Sinsd(f ) causes the replica to appear as two bumps, and attenuation by continuous-time filtering in the PLL causes the bumps to be asymmetric.
The primary artifact seen in Sout(f ) is a bump at 20 MHz that is caused by convolution of the modulation signal, Soutm(f ), with the reference spur. The high relative magnitude of this replica spectrum overshadows the effects of the bumps produced by Φmod(t) in SΦout(f ). It is important to note that the simulation model does not model the finite bandwidth of the loop filter opamp, OP2, which will further
decrease the magnitude of the output power spectrum at high frequency offsets.
11.3.3 Measured Results
Figure 11.15 shows measured plots of SΦtn(f ) and the open loop phase noise of the VCO from the transmitter prototype; the plots were obtained from an HP 3048A phase noise measurement system. In Figure 11.15(b), the binary data stream shown in Figure 11.12 was fed into the LSB of the modulation path to randomize the inter-nal states of the Σ-∆ modulator and reduce spurious content. The resulting spectra compares quite well with the calculated curve in Figure 10.8, especially at high fre-quency offsets close to 5 MHz. At low frequencies, the measured noise is within about 3 dB of the predicted value; the higher discrepancy in this region might be attributed to the fact that i2ch1 was calculated without considering the transient response of the charge pump, and that an offset in the PFD duty cycle may be present. The spur at 20 MHz offset, which is due to the fifty percent nominal duty cycle of the PFD, is less than−60 dBc.