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Phase Locked Loops (PLLs) is a negative feedback system that matches the output frequency to the input frequency. Many applications utilize PLLs such as: frequency synthesizers, skew cancellation, reference clean-up, and clock-data recovery .
For frequency synthesizers, the goal is to generate a clock at a higher speed to that of a slower reference clock. For example, generating a 1 GHz signal from a 100 MHz reference signal. This is a common goal for many optical applications. For example, current work performed by AOSense, a leading research and development company in atomic-level sensing requires clock frequencies well into the hundreds of megahertz and even into the gigahertz range. For this reasons, PLLs, such as the HMC698LP5 from Hittite Microwave are commonly used in their designs.
standard pll design
A basic PLL consist of four main building blocks; Phase Frequency Detector (PFD), Charge Pump (CP), Low Pass Filter (LPF), and Voltage Controlled Oscillator (VCO). Figure 1 is a block diagram of a basic PLL.
Figure 1. Basic PLL Block Diagram 
The PFD detects any differences in phase and frequency of the reference and feedback signals and generates an appropriate 'Up' or 'Down' signal. These signals are then passed to the CP, in which, the CP sources current into the loop filter (Up signals) or sinks current from the loop filter (Down signals). The LPF converts the signal into an analog voltage for the VCO, in which the VCO outputs a clock at either a higher faster or slower frequency based on the 'UP' 'DOWN' signals generated by the PD. This process is repeated until the output frequency of the VCO properly matches that of the reference frequency.
These blocks were constructed and simulated in MATLAB R2112a Simulink.
A. Phase Frequency Detector
As previously stated, PFD are devices that measures the difference between the reference and feedback clocks. There are two commonly used phase detectors: linear and binary. A linear phase detector's output is a pulse signal with a varying width. When the feedback signal is severely out of phase with the reference signal, the pulse width is larger compared to when the two signals are close to being similar. In contrast, a binary (bang-bang) phase detector's output is a fixed pulse width. This binary output signifies if the feedback signal arrived early or late compared to the reference signal.
In this design, a modified version of a linear phase frequency detector was implemented in Simulink, as depicted in figure 2. This PFD generates a logic high for the UP signal when the feedback signal's rising edge arrives ahead of the reference signal's rising edge for the length of the difference. Similarly, when the feedback singal's rising edge arrives after the reference signal's rising edge, a logic high is given for the DOWN signal for the duration of the difference.
M:\SJSU\EE 227\Project\Report Pictures\Figure 2 - PFD.png
Figure 2. Phase Frequency Detector Model
Applying a test signal to both the reference and variable (feedback) inputs and adjusting the feedback signal with some delay, demonstrates the proper functionality of the PFD. This is illustrated in figure 3. The plot is as given from the top down: UP, DOWN, Reference, and Variable CLK.
The UP and DOWN signals are then fed to the charge pump, which directs the loop filter to increase or decrease in voltage, signifying an increase or decrease of the VCO output signal. But first, a discussion on the charge pump and it's modelling is in order.
M:\SJSU\EE 227\Project\Report Pictures\Figure 3 - PFD Test.pngFigure 3. PFD Test Results
B. Charge Pump
The charge pump block in figure 1 is designed to convert the UP and DOWN signals into current for the loop filter. When the UP signal is logic high, the charge pump will source current to the loop filter and when the DOWN signal is logic high, the charge pump will since current from the loop filter.
A circuit representation of a charge pump is given in figure 4 below. From this representation, several key design challenges are noticed. Such as proper current matching from both I1 and I2, parasitic capacitance from the two current sources, and leakage current into and out of the loop filter.
M:\SJSU\EE 227\Project\Report Pictures\Figure 4 - CP.png
Figure 4. Charge Pump Circuit
A Simulink model of a charge pump is given in figure 5. Notice how the DOWN signal is subtracted from the UP signal and then fed into a gain of 0.001. This gain value represents the current of the two current sources. The delay representsrepresents the current of the two current sources. The delay represents the capacitor, Cp, in figure 4.
M:\SJSU\EE 227\Project\Report Pictures\Figure 5 - CP Block.png
Figure 5. Charge Pump Model
Simulating the charge pump model should show a slowly increasing value as long as the UP signal is high more often than the DOWN signal. Figure 6 below shows such a scenario as the CP_Out signal slowly ramps up. This signifies that the VCO will speed up to force the reference signal to catch up to the data signal.
M:\SJSU\EE 227\Project\Report Pictures\Figure 6 - CP Test.png
Figure 6. CP Test Results
C. Loop Filter
A loop filter is an entirely passive component device and consist of two capacitors and a resistors as illustrated in figure 7. The loop filter has two branches, the integral path and the proportional path. The integral path is the C2 branch, while the proportional path is the C1 and R branch. As the name implies, the loop filter filters high frequency noise spurs caused by sampling, but this also adds a pole at 1/RC2 . A resistor in the loop filter provides an isolation phase correction from frequency correction.
M:\SJSU\EE 227\Project\Report Pictures\Figure 7 - Loop Filter Circuit.png
Figure 7. Loop Filter Circuit
A simulink model of a loop filter is given in figure 8 below. The input to the loop filter is connected to the output of the charge pump. The purpose of the loop filter is to take a current and convert it into a voltage, called the control voltage of the VCO.
M:\SJSU\EE 227\Project\Report Pictures\Figure 8 - Loop Filter Block.png
Figure 8. Loop Filter Model
Simulating the loop filter in Simulink gave the plot in figure 9. Re-examining this figure, there may be a an error in the loop filter's output as it's a sawtooth waveform. This will be compared to the VCO output plot for proper functionality in the next section.
Figure 9. Loop Filter Test Results
The final block in figure 1 is the VCO block. There's a slight modification to the VCO block compared to that in figure 1 due to the future use of phase interpolation. Due to this, a phase generator block was required. This phase generator block is given in figure 10.
M:\SJSU\EE 227\Project\Report Pictures\Figure 10 - Phase Generator Block.png
Figure 10. Phase Generator Model
The purpose of the phase generator block is to allow various phases for the phase interpolation PLL in the forthcoming section. For this, the signal is limited to 360 degrees and various phases are generated as illustrated in figure 11. This is the final design of the VCO.
M:\SJSU\EE 227\Project\Report Pictures\Figure 11 - VCO Block.png
Figure 11. VCO Model
A common VCO has a single output, known here as CLK_0. However, due to the use of phase interpolation in the second half of this PLL design, 3 other phases were generated. Each phase separated by 90 degrees.
The feedback to the PDF is derived from CLK_0 signal that is passed through a relay that generates a clock signal from a sinusoidal signal. The final PLL design for the first potion is given in figure 12.
M:\SJSU\EE 227\Project\Report Pictures\Figure 12 - PLL Block.png
Figure 12. PLL Design Phase 1
Testing of the pll
Testing of the PLL consisted of a pulse generator at the reference clock input. This signal was set to 50 Hz is mentioned in . Figure 13 is a plot of the VCO output (CLK_0). The plot shows that in the beginning, the VCO is attempting to lock and after about 30 seconds, the system locks onto the frequency.
M:\SJSU\EE 227\Project\Report Pictures\Figure 13- PLL Test Results.png
Figure 13. PLL Phase 1 Test Results
phase interpolator design
A. Theory Behind Phase Interpolators
Phase Interpolators (PI) is a modified version of a PLL. PIs function by taking a weighted values and multiplying and adding them to two signals shifted in phase at the same frequency. These weighted values are call alpha and beta. Beta equals 1 minus alpha as given in equation (1)
B. Binary Phase Detector
The phase detector used in the PI loop has been modified to act as a bang-bang phase detector instead of a linear phase detector. A modified version of the bang-bang phase detector  was used. This modified bang-bang phase detector is given in figure 13i.
M:\SJSU\EE 227\Project\Report Pictures\Figure 13i- BBPD Block.png
Figure 13i. Modified Bang-Bang Phase Detector
A bang-bang phase detector is different from a linear phase detector since the output signals are fixed pulses and they signify if the feedback clock's rising edge is early or late. Those early and late signals are then fed into a charge pump, which tells the VCO (by means of a loop filter) to go faster or to slow down.
Simulating this modified version of a phase detector was performed in Simulink. The feedback (reference) signal was delayed compared to the DATA clock. This implies that the phase detector outputs a logic high for the LATE signal, in which it does.
M:\SJSU\EE 227\Project\Report Pictures\Figure 13ii- BBPD Test.png
Figure 13ii. Bang-Bang Phase Detector Test Results
D. Quadrature Clocks
Quadrature Clocks are clocks that are separated by 90 degrees. The model to accomplish this was given in figure 11 of the VCO. Testing this with a simple pulse generator input signal provided the plots in figure 14. These plots show four signals that are 90 degrees out of phase with one another.
M:\SJSU\EE 227\Project\Report Pictures\Figure 14- Quad Phases.png
Figure 14. Quadrate Phases
Reading from the top of figure 14 to the bottom, the phases are as follows: 0, 90, 180, and 270 degrees.
To ensure the entire 360 degrees of phases are covered, as given in the VCO, a counter was implemented. For this simulation, an 8-bit counter was used. This implies that for 360 degrees and an 8-bit counter, each degree represents 1.41 degrees of resolution. The importance of this is related to the unit circle. For a count from 0-255, each 64 counts represents a phase shift of 90 degrees.
A simple counter was constructed in Simulink using a just three blocks as shown in figure 15.
M:\SJSU\EE 227\Project\Report Pictures\Figure 15- Counter.png
Figure 15. Counter Model
F. Alpha, Beta, and MUX Values
To determine the alpha, beta, and the MUX values, a model was created in Simulink. From section C, an 8-bit counter was created. Of these 8-bits, bits 0-5 represent the alpha bits and bits 6-7 represent the MUX bits. These bits were extracted and then the alpha and the beta values were obtained as mentioned in section A and equation (1). A Simulink model is given in figure 16.
M:\SJSU\EE 227\Project\Report Pictures\Figure 16- Alpha Beta Mux.png
Figure 16. Alpha, Beta, and MUX Extractor
Testing the model in figure 16 revealed an interesting note. This model was taken directly from  and when a simple test of this block was performed, the MUX bits appeared to be out of the ordinary. It was expected that the MUX values would range from 0-4 as two bits were extracted, giving a four step ramp. However, the four step ramp ranged from 0-192. This is shown in figure 17.
The next section discusses the MUX switching and this is why the issue was noticed. Because of this, this discussion will take place in the next section.
M:\SJSU\EE 227\Project\Report Pictures\Figure 17- Alpha Beta Mux Test.png
Figure 17. Alpha, Beta, and MUX Test Results
G. MUX Model
Since a PI requires the use of two different phases simultaneously, a MUX is required to give the proper signals. In Simulink, a MUX was generated using "multiport switch components'. The model is given in figure 18 below.
As there are four inputs, the select line is required to be a value of 1, 2, 3, or 4 in order to properly select the desired line. The select line is driven by the 2-bit MUX value that was obtained in the previous section, F. This implies that the MUX values should be a 1, 2, 3, or 4 value and not the values that are shown in figure 17. The four steps are correct, but further work is need to properly generate the appropriate select lines.
Due to the MUX select lines not functioning properly, the final PI PLL design was unable to be properly tested. A solution to this problem is to write a piece of code that reads the MUX line and then determines the proper, 1, 2, 3, or 4 value.
M:\SJSU\EE 227\Project\Report Pictures\Figure 18- MUX Model.png
Figure 18. MUX Model
H. Finall PLL Block and Testing
The final design of the complete PLL with the phase interpolator PLL is given in figure 19. As stated in MUX Model section, the MUX line had a critical error that prevented the PLL from being properly simulated. This error was due to the MUX select lines not being of the proper value. If given more time, code would be implemented to resolve this problem or the use of Simulink blocks to generate the proper values for the select lines.
M:\SJSU\EE 227\Project\Report Pictures\Figure 19- Final PLL Block.png
Figure 19. Final PLL Design with PI
For simplicity do to time constraints, a simple test was performed on the final design. Since the MUX select lines are not function properly, a constant value was fed into the select lines to manually pick the phases. When the select line was set to 1 for both, the graph in figure 20 was generated.
M:\SJSU\EE 227\Project\Report Pictures\Figure 20- Final PLL Test - MUX 11.png
Figure 20 PI Output/Feedback Pre Relay
Figure 20 shows that the PLL is working to a degree. Unfortunately, it fails to be properly tested.
PLLs are commonly used devices in a wide range of applications. In this design, a phase interpolator version of a PLL was examined. Although the complete model was successfully constructed in Simulink, the final design was unable to be properly tested. This was due to the malfunction of the MUX select lines that prohibited the simulation to run. A quick work around was implemented, which meant the manual adjustment of the MUX select lines.