High Radio Frequency Signal Generation

Jude Pinto

Mentored by Joe Frisch

07/25/2012

High Radio Frequency Signal Generation

Abstract

Spin Waves are collective excitations that have been observed to oscillate at resonance frequencies in the Super High Frequency range of Radio Frequencies. To study these spin waves, a dedicated timing system is needed to synchronize the X-ray imaging with the high frequency Spin Wave oscillation. An RF circuit using frequency modulation and a phase-locked feedback loop will provide this synchronization. The frequency multiplication creates the harmonic frequency modulated from the X-ray imaging signal and the feedback loop holds the modulated signal locked to the desired frequency. This RF circuit produces jitter between the output signal and the desired signal that is less than one order of magnitude of the X-ray imaging resolution. An RF circuit providing dedicated timing through harmonics of the imaging signals, as well as a feedback loop to eliminate error, provides a stable synchronization between Spin Wave oscillation and Synchrotron Radiation X-ray imaging.

Introduction

A Radio Frequency (RF)circuit will be used to take a 476 MHz input signal originating inthe Stanford Synchrotron Radiation Lightsource (SSRL) and generate a high frequency,harmonic signal with a subharmonic offsetto drive an oscillating microwave field that will cause electron-based magnetic excitationin the molecules of a thin film magnetic material. The SSRL produces X-rays from electrons accelerating centripetally in a storage ring. These X-rays will be used as the imaging component to the experiment using the RF circuit.This experiment conducted by collaboratingresearchers involves magnetic material excitation. By exciting the material via a microwave field, propagations called spin waves are produced within the material. A spin wave is a movement of magnetic spin moment directions across a molecule. On a ferromagnetic material, the spin of the electronscreate a net magnetic moment for the material. This uniform magnetic moment direction gives the material magnetic properties. Elements such as nickel, cobalt, and iron are the only periodic table elements containing ferromagnetic properties, and therefore, are the only elements that are considered magnetic. The particular test material used is called Permalloy, which has a chemical composition of Ni80Fe20. The microwave field changes the constant direction of the vertical spin moments to an oscillating behavior, collectively, also a spin wave. These spin waves will be captured by the Scanning Transmission Electron Microscope (STXM) to image the material excitation. The excitations occur at high resonance frequencies in the range of 5 GHz-10GHz, which is the Super High Radio Frequency Range. Several frequencies will be used in the range of resonance frequencies to create these excitations in the material. These frequencies will be generated as a harmonic of the original X-ray pulse frequency. In addition to creating a harmonic, a subharmonic offset will be addedto the high-frequency harmonic to allow the detector to sample several different phases of the excitation.Once the modulated frequency is generated, a feedback loop will be used to keep the output signal,which is transmitted to the experiment, locked to the desired frequency value.This RF circuit provides high frequency signals to a system requiring accurate timing between the imaging X-rays and the microwaves used for the experiment.

Methods

Using the SSRL, X-rays will be used to create images of the material’s spin waves. Electrons accelerate centripetally in the SSRL bend at turns on their path through the ring. At each turn, X-rays are emitted. With these X-rays, the reference frequency of the input signal is derived and the images of the material will be obtained. Once the X-rays interact with the material, the interactions will be observed through an X-ray microscope.

The imaging software used to capture the magnetic moment oscillations is a Scanning Transmission X-ray Microscope (STXM). As mentioned, there is a net magnetic moment for a ferromagnetic material. This net magnetic moment can be visualized by magnetic moments of each atom pointing in the same, upward, vertical direction, as shown in Figure 1. When the microwave field deflects the magnetic moments of the molecules, there is a vertical component between the tip of the moment at the vertical position and the tip of the moment at its deflected position, as demonstrated in Figure 2. Using a STXM, this vertical difference can be measured.Once this difference is measured, a collective oscillation of the material’s magnetic moments has been demonstrated.

The reference signal, which has a frequency of 476 MHz, being taken from the SSRL will be multiplied in frequency and offset by a subharmonic of the reference frequency. Using only a harmonic frequency to drive the microwaves would give us the same image, as shown in Figure 3. To solve this problem, a subharmonic offset will be added to create oscillation phases. This correction and the phases of oscillation are shown in Figure 4.With this offset from the reference frequency, the X-rays will be taking images at different times during the oscillation. Depending on the integer factor of the reference frequency, the amount of images that are collected will together create an image of one oscillation, with the amount of images being the integer factor.

An RF circuit that generates a high frequency harmonic of the reference signal, with a subharmonic offset, will be used to time the X-rays with the microwave field. Radio Frequency components will be used to manipulate and modulate this signal. These components that comprise the RF circuit are frequency multipliers, frequency dividers, amplifiers, frequency mixers, power splitters, and high-pass and low-pass filters. These components will be assembled into a circuit design, shown in Figure 5, and used to create the desired output signal.

To modulate the reference frequency, frequency multipliers and dividers will be used.Respectively, these components will multiply a lower-frequency signal to a higher-frequency harmonic of the reference signal and divide a higher-frequency signal to a subharmonic of the reference signal. To supplement the multipliers and dividers, amplifiers raise the power of the signal to compensate for the power loss in the multiplication process. Also, an amplifier after the divider will raise the power of the signal coming out of the divider to bring the signal up to the same power as the signal coming out of the multipliers. To filter out lower frequency noise created by previous subharmonics left in the signal, a high-pass frequency filter is inserted in the circuit path after the last amplifier following the final frequency multiplier to obtain only the desired frequency. With the two signals at the same power, a frequency mixer may now be used to obtain the desired frequency.

Once the high-frequency harmonic and low frequency subharmonic are obtained, mixers are used to combine these signals. Mixing signals is a multiplication process that entails two input signals that produce two frequencies at the sum and difference of the inputs. As shown in Figure 6, the high frequency is offset by the lower frequency to produce the sum and difference of the two frequencies. In the particular case of the circuit, the sum of the two frequencies will be used to create a high frequency harmonic signal with a subharmonic offset.

In addition to these components within the circuit, instruments are used to test the circuit, once the high frequency signal is generated. Spectrum analyzersmeasure the output signals in the experiment and will analyze the spectrum of frequencies contained within the output signals. To simulate the reference signal from the SSRL, a frequency synthesizer generates an artificial signal that has the same frequency as the signal from the SSRL ring. Another frequency synthesizer will be used in testing the circuit and in the experiment.This second synthesizer will create a signal locked to the desired frequency and is the main component for the frequency locking part of the circuit called the phase-locked loop.

A feedback loop will be created with a mixer, this frequency synthesizer, and aPID controller to create picosecond-stability for the output signal. This feedback is termed a phase-locked loop, because the loop detects the phase of the input signal and generates a subsequent frequency to mix with the input signal, creating an output signal that will continually keep the phase of the looping signal locked to fixed time intervals. As shown in Figure 7, the phase-locked loop consists of an input and feedback signal being fed into a phase detector, a loop filter, and an oscillator. The second mixer in the circuit, shown in Figure 5 after the first mixer in the Frequency Generation section, generates a low-frequency signal, which is fed through a low-pass filter to attenuate the high frequency harmonic noise, and then into the phase detector. The phase detector finds the phase difference between the input signal and the signal from the frequency synthesizer. This difference is fed into a loop filter and translated into a readable input for the frequency synthesizer. This input causes the synthesizer to produce a new oscillating signal so the phase is aligned to the desired frequency.

Now the desired frequency has been generated, as well as locked, the signal is fed into outputs. One output is the Beat Out section shown in Figure 5. This output produces the subharmonic frequency from the divider and checks if we are at the right subharmonic frequency. The second output is fed to drive the microwaves for the Spin Wave experiment.

The design for the circuit in Figure 5 needs to be constructed and fit into a circuit box. The arrangement of components will be defined by the order of the different configurations and which amplifier is compatible with the various frequency multipliers. Other tasks to assembling the circuit are adjusting the frequency of the oscillator to the actual frequency of the synchrotron and checking to see if the multipliers work outside of their input frequency range.

Results

The final look of the circuit is shown in Figure 5. There is little space for the cables, so right angle adaptors were used to more easily switch between different multiplier configurations.

Unfortunately, the experiment could not obtain evidence, because the sample to be tested for spin waves was not constructed correctly. The process attached layers of Ni80Fe20, Copper, Cobalt, and another layer of Copper. The layer of Permalloy was oxidized during the fabrication of the material. Since the material was ruined, the experiment could not be finished. However, the circuit will be ready to use when the experiment is up and running worked, because the circuit worked during testing.

For each of the five configurations of multipliers, the spectrum analyzer showedthe circuit generated the desired frequency for all configurations. All unwanted subharmonic frequencies were attenuated through the high-pass filters. The highest noise was with the fifth configuration of two frequency doublers and the 5x multiplier. A subharmonic of 952MHz was generated when the desired frequency was 9520MHz. A High Pass filter was inserted after the 5x multiplier to attenuate the power for that frequency in the signal. This filter was used for the Configuration 4 to eliminate any unwanted noise coming from the 5x multiplier in that setup. With enough noise decreased, the spectrum analyzer showed a signal that had the desired frequency at a power higher than 10 dB, in each configuration.Since the frequency had a power of 10 dB higher than any of the other frequencies, this frequency would be the majority of the signal and recognized as the signal’s frequency at any input.

As mentioned, a high pass filter was added in the multiplier configurations, and low pass-filters were added after the second and third mixers. With these filters, the PID controller was able to lock onto the desired frequency and generate a consistent output of the right frequency. The accuracy of this signal is defined by the jitter from its desired position.

The oscillator in the feedback loop produces an output frequency close to the desired frequency. That frequency is maintained close to the locked position through the feedback loop. How close the frequency is to the desired frequency is a judge of how well the whole system is performing. Jitter is the measure, in seconds, of signal variation from its regular periodicity. To measure the jitter, the amplitude of the locked and unlocked sine wave is necessary to know, as well as the frequency of the original signal. The derivation of the simplified equation used to calculate jitter is shown in the Appendix.

The jitter of each frequency is listed in Table 1. All the jitter values were found inside the 10-13second range. The largest jitter is 740 femtoseconds for the configuration of two 2x multipliers and one 3x multiplier. This jitter is less than 10% of the 10 picosecond X-ray imaging resolution.

Conclusions

The jitter of the system defines how well the system works. As mentioned, the largest jitter produced by the circuit is less than 10% of the 10-picosecond resolution of the X-ray imaging. Since the jitter is an order of magnitude less than the resolution, the circuit provides a signal close enough to the desired frequency.

To improve the circuit, an op-amp may be integrated into the system to provide a simpler solution to the feedback loop. Proportional and integral controllers are a general solution of error elimination to the loop. An op-amp would provide a better solution, because lead-lag control is specific to the purpose of the phase-locked loop. There would be a single gain to be changed, instead of multiple gains for the different controllers. Also, the op-amp could be integrated into the circuit easier than the large PID module.

Another possible simplification would be the replacement of the string of multipliers and amplifiers with a single component. A comb generator would create all harmonics up to the input signal’s 25th harmonic. Inserting a comb generator into this circuit would eliminate the need for the frequency multipliers and amplifiers in the frequency generation stage. This substitution would create more space in the circuit box, allowing space for another component, such as the op-amp.

Appendix

Two sine waves with the same angular frequency offset by an incremental change in time:

(1)

(2)

where t=time, = angular frequency

Mixing the signals gives the multiplication of the two waves

Higher frequency too high to observe, not of interest, so equation becomes:

=

By the Small Angle Approximation, and direction is arbitrary, so the sign of the product does not matter. The equation reduces to:

Taking the derivative with respect to to observe the frequency response,

Since ,

,

where is the jitter of the output signal from the desired signal.

Tables

Frequency (MHz) / 5791.33 / 7219.33 / 7695.33 / 8647.33 / 9599.33
Mixed Signal Voltage (Volts) / 3.3 / 4.3 / 1.5 / 3.03 / 1.3
Amplitude Signal (Volts) / 245 / 700 / 360 / 170 / 180
Jittter (seconds) / 7.40E-13 / 2.71E-13 / 1.72E-13 / 6.56E-13 / 2.39E-13
% error to 10 picoseconds / 7.4% / 2.7% / 1.7% / 6.6% / 2.4%

Table 1 – Values Used to Calculate Jitter and the Value for Jitter for Each Frequency

Figures

Figure 1 – A Ferromagnetic Material with the stronger magnetic moments pointing in the vertical direction, creating a net magnetic direction in the upward direction (Image Courtesy of Gale Martha/Scientific Explorer)

Figure 2 – A Ferromagnetic Material Excitation showing the Vertical Magnetic Moment in a Solid Green Arrow (shown here horizontal) and the Deflected Position shown in a Dotted Green Line, of Which the Components that Can Be Measured Shown in Red and Blue

Figure 3 – A Harmonic Signal Driving the Microwaves for the Experiment and Producing the Same Image Captured by the X-rays (Image: Jens Böning via Wikimedia Commons)

Figure 4 – A Harmonic Signal with Offset Driving the Microwaves for the Experiment and Producing the Phases of the Oscillation (Image: Jens Böning via Wikimedia Commons)

Figure 5 – The RF Circuit Design Showing the Three Sections for Frequency Generation, Phase Lock to the Desired Frequency, and Signal Outputs

Figure 6 – Mixing of Two Signals, One of High Frequency and the Other of Low Frequency, to Create a Sum Frequency and Difference Frequency of the Two Frequencies

Figure 7 – Diagram of a Phase-Locked Loop Showing the Phase Detector, Loop Filter, and Oscillator