Update non_linear_analysis.md
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# Non-Linear Simulation
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At this stage, we extend our simulations into the non-linear domain, as linearity is a critical factor in power amplifier design. To assess this, we need to determine the **P1dB compression point**, which indicates when the amplifier starts deviating from linear operation. Additionally, we will perform a **load-pull analysis** to optimize the output match for high linearity.
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For non-linear simulations, **Ngspice** is no longer sufficient, as it does not support **harmonic balance analysis**, which is essential for capturing the non-linear behavior of RF circuits. Instead, we use **Xyce**, which provides the necessary non-linear simulation capabilities. However, Xyce lacks robust internal match calculations and graphing tools, making post-processing necessary. To overcome this, all data analysis and visualization will be handled through **Python scripts**, which process simulation results on the fly. The required scripts are available in the repository and should work seamlessly if schematic labels and naming conventions are followed consistently.
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Since non-linear simulations often require **input power sweeps**, but Xyce does not directly support this functionality, we will implement a workaround using a **sinusoidal current source** in combination with a fixed load resistance to vary the power level
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### Setting Up the First Testbench
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For the first testbench, we continue from the previous schematic and modify it for non-linear simulation. Since we are now using Xyce models, we must specify a different library file for the HBT transistors. The correct path to the model library is:
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```
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/../../IHP-Open-PDK/ihp-sg13g2/libs.tech/xyce/models/cornerHBT.lib
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```
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Additionally, we need to instantiate two key components:
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1. **Harmonic Balance Analysis Block** – Required for frequency-domain simulation of non-linear behavior.
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2. **Parameter Sweep Block** – Used to step through different operating conditions, such as varying input power.
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The setup for these components is illustrated in the image below:
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<p align="center"> <img src="../../../media/module_2/harm_balance_1.png" width="300" height="200" /> </p>
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### Configuring the Parameter Sweep and Harmonic Balance
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_(Note: The Harmonic Balance block is only visible when the Xyce simulator is enabled.)_
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As shown in the image above, the **parameter sweep** is configured as follows:
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```
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SW1
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sim=HB1
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Type=lin
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Param=y
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Start=0.0001
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Stop=0.05
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Points=51
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```
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_(make sure that the step size is a n natural number)_
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This setup defines a **linear sweep** for the parameter **y**, ranging from **0.0001 to 0.05** with **200 points**. This will allow us to analyze how the amplifier responds over a range of input conditions.
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For the **Harmonic Balance** analysis, the key parameter **n** is set to:
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$$n=5n$$
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The complete schematic setup for the non-linear analysis, including all relevant components, is shown in the image below:
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<p align="center"> <img src="../../../media/module_2/harm_balance_2.png" width="600" height="500" /> </p>
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_(Remember to set the frequency of sources and components accordingly.)_
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In this setup, we define a **parameter** named **y** with a default value. This parameter is essential for performing the input power sweep, but the value of y specified in the param section is unimportant in this case.
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As seen in the sweep configuration, we vary the **input current** from **0.0001 A to 0.05 A** through a **constant 50Ω resistor**. This corresponds to an **input power range of -33 dBm to 21 dBm**.
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This sweep is crucial for evaluating the amplifier's behavior in the **non-linear region**, allowing us to determine its **1 dB compression point (P1dB)**—a key metric for assessing linearity.
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### Running the Simulation and Verifying Results
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At this stage, we can proceed with running the simulation. Once the simulation is complete, the first step is to **instantiate a table** to inspect the results and ensure that the output data is correctly formatted.
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In the table, we should observe **10 data points** for each swept parameter, corresponding to the **harmonic components**, both **positive and negative**. This confirms that the simulation is correctly capturing the harmonic balance response.
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The expected table output is shown below:
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<p align="center"> <img src="../../../media/module_2/harm_balance_3.png" width="350" height="400" /> </p>
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### Processing the Simulation Data
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As seen in the results table, the simulation has run successfully. This confirms that the **sweeping parameter**, **frequency axis**, and **raw data** are correctly recorded.
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Within the **part_3_non_linear_analysis** section, a folder named **python** contains a script designed to facilitate post-processing. This script aims to provide an easy way to **plot gain vs. input power** and **output power vs. input power**.
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**Note:** There may be potential issues with the script, so adjustments might be required depending on the data format or specific cases encountered.
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To use the script, navigate to its location and run the following command:
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```
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python3 plot_xyce.py
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```
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this will print the following information, to show functionality:
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```
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This script processes and extracts variables from a specified dataset file.
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You can use the script in the following ways:
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1. To list all independent and dependent variables in the dataset:
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python3 script.py <file_path>
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2. To print all values for a specific variable:
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python3 script.py <file_path> <variable_name>
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3. To run the analysis and generate plots, pass the following arguments:
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python3 script.py <file_path> <vout_var> <vin_var> <iin_var> <iout_var> <sweep_var> <freq_interest> [xlim_min xlim_max]
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```
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From here, navigate to the simulation directory containing the dataset file and execute the following command:
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```
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python3 ../../python/plot_xyce.py load_pull.dat.xyce "V(VOUT)" "V(VIN)" "I(PR2)" "I(PR3)" "Y" 50e9 -30 -10 -1 16
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```
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This command generates a readable plot of **gain vs. input power**. For **output power vs. input power**, adjust the boundaries accordingly.
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If the naming conventions of the variables differ in your schematic, use the following command to list all available parameters in the dataset:
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```
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python3 ../../python/plot_xyce.py load_pull.dat.xyce
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```
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Once the script runs successfully, the **gain vs. input power** plot should resemble the following:
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<p align="center"> <img src="../../../media/module_2/gain_vs_input_power_2.png" width="600" height="500" /> </p>
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<p align="center"> <img src="../../../media/module_2/output_power_vs_input_power.png" width="600" height="500" /> </p>
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## Performing Load Pull
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As observed in the previous simulation using ideal output components, the **1 dB compression point** was approximately **-7.88 dBm**. To optimize the output network, we aim to maximize the circuit's **linearity**. However, since sweeping a **complex impedance** (i.e., a±bia \pm bia±bi) is not straightforward, we instead perform a **resistive sweep** at the output and determine which resistance yields the best linearity.
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While this approach requires some manual adjustments, the **Python script** can assist in processing the results. The exact method is left to the user’s preference. In the following example, we analyze the compression point around a **50Ω termination** and identify the most suitable resistance.
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It is important to avoid **excessively low resistance values**, as this would degrade the amplifier’s characteristics significantly. Below, the schematic illustrates the setup for a **40Ω termination**:
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<p align="center"> <img src="../../../media/module_2/harm_balance_4.png" width="600" height="400" /> </p>
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Gain curve and compression point was seen as the following:
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<p align="center"> <img src="../../../media/module_2/gain_vs_input_power_2.png" width="600" height="500" /> </p>
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### Evaluating the Compression Point Shift
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As observed, adjusting the termination has **moved the compression point upward**.
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#### **Implications for the Termination Network**
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This result suggests that **matching to a 40Ω termination improves the circuit’s linearity**. However, modifying the output match inevitably **affects the input match** and alters the **reflection coefficients**. This presents a trade-off, and it is left to the reader to determine an optimal matching network.
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#### **Recommended Approach**
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- Do a matching assuming no influence on input reflection.
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- **Gradually tune** the network components to achieve the highest possible **P1dB** while maintaining a good match.
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The schematic below illustrates the circuit configuration that will be used in further analysis. The corresponding **gain response** is shown in the final image.
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<p align="center"> <img src="../../../media/module_2/harm_balance_5.png" width="600" height="400" /> </p>
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![[harm_balance_5.png]]
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<p align="center"> <img src="../../../media/module_2/gain_vs_input_power_3.png" width="600" height="500" /> </p>
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![[gain_vs_input_power_3.png]]
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