Chapter 2 Feedback Loop Oscillators with Piezoelectric Resonators…. 7
2.3 Voltage-Controlled Oscillator with FBAR Resonator
2.3.3 Measurement and Discussion
The fundamental and higher harmonics oscillation spectrums were measured and shown in Fig. 2-20 (a) and (b), respectively. The 2nd harmonics of oscillator is suppressed below 40 dB as shown in Fig. 2-20(b). The oscillation frequency is slightly higher than the series resonance frequency fS of FBAR because of the parasitic capacitance from package effect. The variation of fundamental frequency with temperature was also measured and shown in Fig. 2-21. The TC of oscillator is about -34.5ppm/oC and seems to be equal to that of FBAR. It implies that the effective tank of the oscillator is dominated by the FBAR resonator. The tuning characteristic is shown in Fig. 2-22 with ±6% range. The performances of the oscillator with FBAR resonator are measured and summarized in Table 2.3.
Table 2.3: Measured Results for the FBAR oscillator.
Item Value Supply Voltage (Volts) +5.0
Supply Current (mA) 65
Output Power (dBm) +14.5 Tuning Voltage (Volts) 0-5
Tuning Range > ±6%
Sub Harmonics (dBc) -40
(a)
(b)
Fig. 2-20 (a) Output fundamental spectrum, and (b)harmonics spectrum for the oscillator.
10 20 30 40 50 60 70 80 2430
2440 2450 2460 2470 2480 2490 2500 2510
Frequency (MHz)
Temperature(°C)
fp(FBAR) Oscillator fs(FBAR)
Fig. 2-21 Measured variation of fundamental frequency with temperature for FBAR and oscillator.
Fig. 2-22 Output frequency vs. tuning voltage
Chapter 3
Measurement and Prediction of Phase Noise in Oscillator with STW Resonator
3.1 Introduction
Frequency stability can be defined as the degree to which an oscillating source produces the same frequency throughout a specified period of time. Every RF and microwave source exhibits some amount of frequency instability. This stability can be broken down into two components: one is long-term stability, the other is short-term stability. Long-term stability describes the frequency variations that occur over long time periods, expressed in parts per million per hour, day, month, or year. Short-term stability contains all elements causing frequency changes about the nominal frequency of less than a few seconds duration. Here, we just focus on the short-term stability.
Phase noise is the important specification for an oscillator. The absolute phase noise of an oscillator is set by the residual noise of the active devices, the residual noise of the resonator and the bandwidth of the resonator. Generally the active devices in the oscillator are the major noise contributors. In the design phase, we found that the active devices with lower noise figure could not always lead to the oscillator with lower phase noise. After examining the residual phase noise of the major components in the oscillator, we found the residual phase noise of the STW resonator dominates the phase noise of the oscillator instead of the active devices and the lower noise figure of active devices do not relate to the lower residual phase noise.
Here, the Agilent’s E5503B phase noise measurement system is used for residual phase noise and absolute phase noise measurements. A phase noise prediction method based on residual phase noise of devices in oscillators is presented in this chapter.
3.2 Residual Phase Noise of Devices
3.2.1 Residual Noise
Residual noise (or two-port noise) is the noise added to signal when the signal is processed by a two-port device. Such devices include: amplifiers, dividers, filters, mixers, multipliers, phase-lock loop synthesizers, or any other two-port electronic networks. Residual noise contains both AM and PM components. [42-44]
There are two basic noise mechanisms in residual noise: one is additive noise, the other is multiplicative noise. Residual noise is the sum of additive and multiplicative noise. Additive noise, as shown in Fig. 3-1, is generated by the two-port device at or near the signal frequency and added in a linear fashion to the signal.
Multiplicative noise has two known causes. One is an intrinsic, direct phase modulation with 1/f spectral density and the exact origin of this noise component is unknown. The other is noise may modulate an RF signal by multiplying baseband noise with the signal, as shown in Fig. 3-2. This mixing is due to any non-linearities in the two-port network. The baseband noise may be produced by the active devices active devices of the internal network, or may come from low-frequency noise on the signal or power supply.
Fig. 3-1 Additive noise component.
Fig. 3-2 Multiplicative noise component.
3.2.2 Measurement Process of Residual Phase Noise
The basic residual phase noise measurement setup is shown as Fig. 3-3. An unmodulated signal source with low AM noise is necessary. The AM noise of the source which used for residual phase noise measurement must be comparatively small because the mixer type phase detector has only 20 to 30 dB of AM noise rejection. If the AM component of the source is greater than 20 to 30 dB above the residual phase noise of the device-under-test (DUT), it will contribute to the residual phase noise measurement and show the residual phase noise as being greater than it really is. The noise floor of measurement system is established by replacing the DUT with a feed-through and adjusting the total insertion loss in the device test path to maintain the proper RF signal power level to the R-port (LO-port) of the phase detector. Phase quadrature for two input ports of the phase noise detector is established by using a mechanical line stretcher. The electronic phase shifter is not proper because of its high residual noise. A critical point is to maintain the constant RF power level to the L-port (device test path) and R-port for the phase detector during calibration as well as during the actual measurement. The source noise in each of the two phase detector paths is correlated at the phase detector for frequency offset range of interest. When the source noise is correlated at the phase detector, the source phase noise cancels, leaving only the residual phase noise of the DUT. Agilent E5503B noise measurement system is used for the residual phase noise measurement. Fig. 3-4 shows the E5503B connection diagram for residual phase noise measurement and the system noise floor is shown in Fig. 3-5. The spurious signals which closed to the carrier are the system spurious, primary 60 Hz (and harmonics) power line spurs.
A bandpass filter type response will cause the source noise to be decorrelated at the edge of the filter. This decorrelation of noise causes the system to measure the source noise level directly at the offsets beyond the filter bandwidth.
Fig. 3-3 The basic setup for residual phase noise measurement.
Fig. 3-4 The E5503B connection diagram for residual phase noise measurement. [44]
Fig. 3-5 Measured noise floor for residual phase noise measurement system.
3.2.3 Residual Phase Noise of Main Components in Oscillator
There are three major noise contributors in this feedback loop oscillator: STW resonator, loop amplifier and electronic phase shifter.
Residual phase noise in a SAW or STW resonator occurs when an unmodulated carrier is passed through the acoustic device. In this process, phase fluctuations which occur in the resonator cause a direct phase modulation of the carrier so that it appears with PM modulation noise sideband at the device output.[43] The residual phase noise of the STW resonator is shown in Fig. 3-6. It is measured by applying the power approximately the same power level in the steady state oscillation condition. The corner of the flick noise is out of the scope of this measurement.
Fig. 3-6 Residual phase noise of STW resonator.
The residual phase noise of the loop amplifier is shown in Fig. 3-7. The noise floor is approximately -170dBc/Hz with a 1/f flicker noise corner at 17 kHz. Noise figure is the ratio of the output noise of an amplifier referred back to the input divided by the thermal noise floor. Noise figure is a common specification that is used to calculate the noise at Fourier frequencies f that are far from the carrier frequency. The noise figures listed in the data sheets of actives devices are small signal noise figures, not dynamic noise figure. The dynamic noise figures are measured under actual large signal conditions and may differ from the small signal noise figures. It includes the multiplicative noise produced by the non-linearities of active device, in the presence of a large signal. In the presence of a carrier signal, the noise level is no longer
constant but often increases as f decreases. This increase usually changes at a rate of at least 1/f, “flicker” behavior, which often significantly dominates over the white-noise level given by the NF, which in practice is measured in the absence of an actual signal through the amplifier. Furthermore, the flicker- noise level depends on the amplifier’s linearity and input power. Because of this signal induced rise in amplifier noise, many systems do not achieve the performance predicted by using the no-signal NF characterization. The dynamic noise figure can be expressed as:[45]
in
TH P
N
f − +
=L( ) NFD
Where NFD is the dynamic noise figure in dB, NTH is the thermal noise, Pin is the input signal power in dBm, and the L(f) is the residual phase noise in dBc/Hz.
Fig. 3-7 Residual phase noise of loop amplifier.
The electronic phase shifter is mainly constructed varactors and inductor. The varactors are the noise contributors. The residual phase noise performance for the electronic phase shifter is measured and shown in Fig. 3-8.
Fig. 3-8 Residual phase noise of electronic phase shifter.
3.3 Absolute Phase Noise of Oscillators
The phase noise test characterizes the output spectral purity of an oscillator by determining the ratio of desired energy being delivered by the oscillator at the specified output frequency to the amount of undesired energy being delivered at neighboring frequencies. This ratio is usually expressed as a series of power measurements performed at various offset frequencies from the carrier. The power measurements are normalized to a 1 Hz bandwidth basis and expressed with respect to
the carrier power level.
3.3.1 Phase techniques of absolute phase noise measurements
There are three dominant techniques used to measure the phase noise of oscillators: the direct spectrum analyzer approach, the phase-lock-loop (PLL) techniques, and the discriminator techniques.[46] The most direct and probably the oldest method used to measure the phase noise of oscillators is the direct spectrum analyzer method. Here the signal from the device-under-test (DUT) is input to a spectrum analyzer tuned to the DUT frequency. The sideband noise power can be directly measured and compared to the carrier signal power to obtain the phase noise spectrum. This method actually measures the total sideband noise, including AM noise and phase noise. If AM noise is much less than the phase noise, the measurement can be considered as to be the phase noise. The sensitivity of this method is limited by the internal local oscillator (LO) noise of the spectrum analyzer, and the inability to track any signal drift limits the close-to-carrier noise measurement capability of the analyzer.
When the AM noise is relatively high to the phase noise, a phase detector is required to separate the phase noise from the amplitude noise. The phase detector converts the phase difference of the two incident signal in to a voltage at the output of the detector. When the phase difference between the two input ports of the detector is set to 90 degree, the voltage output will be zero volts. Any phase fluctuation from quadrature will result in a voltage fluctuation at the output. When the quadrature is not maintained, an error can be introduced into results based on the amount of the phase delta from quadrature. The error is 20 log [cos (phase deviation from quadrature)] (dB). Phase detectors are usually constructed by the double balanced mixers, and typically required large power signals at the input port to operate properly.
One of the signals must be of high power to switch the diodes in the detector, allowing the other signal to be of lower power.
There are two different measurement techniques which use a phase detector, along with associated filters, low noise amplifier, and baseband analyzer: one is the PLL with reference source measurement technique, and the other is FM discriminator measurement technique. Within the PLL with reference source measurement technique, another source is used to provide the reference phase signal for the phase detector. This is the standard measure of phase fluctuations described in NIST Technical Note 1337. Fig. 3-9 shows a block diagram of the method suggested by NIST.
Fig. 3-9 General block diagram described in NIST technical note 1337.
Signals from two oscillators at the same nominal frequency are applied to the mixer inputs. The PLL is used to controlled either of the two sources and establish phase quadrature at the input ports of the phase detector. This means that one of the two sources used in this method must have DC voltage control capability for phase
locking. A very narrow band PLL is used to maintain a 90 degree phase difference between these two sources. The phase detector operation is such that when the input signals are 90 degrees out of phase (in quadrature), the output of the mixer is a small fluctuating voltage proportional to the phase difference between the two oscillators.
By examining the spectrum of this error signal on the spectrum analyzer, the phase noise performance of this pair of oscillators may be measured. If the noise of one oscillator dominates, its phase noise is measured directly. A useful and practical approximation when the two test oscillators are electrically similar is that each oscillator contributes one-half the measured noise power. When three or more oscillators are available for test, the phase noise of each oscillator may be accurately calculated by solving simultaneous equations expressing data measured from the permutations of oscillator pairs. The frequency difference between the two sourced at the phase detector must be less than 10% of the peak-tuning-range (PTR) for PLL to close. High PTR will cause the increase in the system noise floor. This feature makes this technique is not suitable for measuring the high-drift-rate low phase noise sources which requires high PTR. Lower power from the DUT or the reference source can cause the phase detector noise floor to rise or the phase detector to not operate. Low noise amplifier prior to the phase detector can help to solve this problem, but the residual noise of the amplifiers will add to the phase detector phase noise floor. The increase in the system noise floor will degrade the sensitivity of the phase detector.
The residual noise of the amplifier becomes a limiting factor in the overall system measurement noise floor.
The oscillators with SAW or STW resonators have both low phase noise and high drift rate characteristics. So, the direct spectrum techniques and the PLL with reference source measurement techniques are not fulfilling the requirement while measuring the low phase noise oscillator with piezoelectric resonator. FM
discriminator technique is the hopeful candidate for measuring these low phase noise SAW oscillator. The theory and design consideration are describe as follows.
3.3.2 Theory of FM discriminator [46,47]
The basic block diagram for frequency discriminator is shown as Fig. 3-10.
Unlike the PLL phase detector method, the frequency discriminator method does not require a second reference source phase locked to the source under test. This makes the frequency discriminator method extremely useful for measuring sources those are difficult to phase lock, including sources those are microphonic or drift quickly. It can also be used to measure sources with high-level, low-rate phase noise, or high close-in spurious sidebands, conditions with can pose serious problems for the phase detector method. A wide-band delay line discriminator can be implemented using a low loss coaxial cable. A resonator can also be applied for the narrow-band delay line discriminator. Delay line discriminators are only capable of measuring phase type random noise and are in fact insensitive to AM noise. Typically AM rejection for the delay line discriminator is greater than 20dB.
Fig. 3-10 Basic block diagram for frequency discriminator.
A delay line and a mixer operating as a phase detector have the combined effect of a frequency discriminator. The delay line transforms any frequency fluctuation into phase fluctuation and the mixer with L and R inputs at 90 degree offset linearly converts the phase fluctuations into voltage fluctuations at the IF port. Fig. 3-10 shows the basic block diagram of frequency discriminator. The theory can be derived as follows:
The source under test can be represented as
[
( )]
function describing the phase fluctuation with time.Equation (1) can be expanding as:
[
cos cos ( ) sin sin ( )]
)
(t A t t t t
Vs = o ωc φ − ωc φ (3.2) When the phase noise is treated as narrow band phase modulation, the magnitude of
)
Where L is the insertion loss of power splitter. s
We can get VL(t) and VR(t) which are the input signals of the L-port and R-port for the mixer type phase detector respectively,
[
( ) ( )]
Where LDis the insertion loss of delay line.
The mixer output signal Vm(t) can be express as:
After passing through the low pass filter and low noise amplifier, the output signal )
Where Lm is transfer gain of the mixer, and G is the sum of insertion loss of low pass filter and the gain of the low noise amplifier.
If 2 Here, the output signal Vo(t) is proportional to the phase differenceφo(t)=
[
φ(t)−φ(t−τ)]
. Therefore the sensitivity to the phase noise of the source is:τ πfm ensivity 2sin
S = (3.6) where fm is the offset frequency, and τ is the delay time.
3.3.3 Frequency Discriminator System Setup
The frequency discriminator is used to measure the phase noise of the oscillator with STW resonator. The delay line frequency discriminator is implemented with Agilent’s E5503B phase noise measurement system and a delay line. The connect diagram for this system is shown in Fig. 3-11. The key element in the design of delay line discriminator is the delay line itself. For accurate phase noise measurements, it was shown that the delay time τ must be chosen such that is the maximum frequency of the components to be measured. A 312ns delay line implemented by an ANDREW LDF5-50A low-loss coaxial cable is used in this measurement. Long enough delay time is needed to ensure the sensitivity of the measurement system. In Fig. 3-12, it reveals the system noise floor and the null points of the frequency discriminator. The sensitivity of the discriminator techniques is approximately equal to the phase detector system sensitivity at the offset frequency
πτ LNA noise and therefore does not have
x x
sin -type response. Increasing the length of
the delay time improve the close-to-carrier noise floor but reduces the power to the phase detector. It also reduces the maximum offset frequency that can be measured with no
x x
sin correction.
Fig. 3-11 Connect diagram of Agilent E5503B for FM discriminator technique. [44]
Fig. 3-12 The measured system noise floor and the null points for FM discriminator.
3.4 Prediction of Phase Noise
A feedback loop oscillator with STW resonator is presented in section 2.2. For comparison, the measured absolute phase noise of the oscillator and the residual phase noise of main components for the oscillator, including loop amplifier, electronic phase shifter, and STW resonator, are shown in Fig. 3-13. The spectral shape of the oscillator (curve 1) indeed arrears 1/f3 near the carrier. The intersection point with 1/f curve is around 50 kHz offset. The magnitude at 100 kHz offset is -153dBc/Hz.
Fig. 3-13 Measured phase noise for the 2488.32 MHz STW oscillator.
To analyze the shaping behavior of the close loop, the residual phase noises are
To analyze the shaping behavior of the close loop, the residual phase noises are