nathan/Negative-Resitance-CRLH-Calculations
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Fix DOI reference and formatting in README

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Updated DOI reference and improved formatting in the README.
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Nathan Chordas-Ewell
2026-02-19 17:17:45 -05:00
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@@ -1,7 +1,7 @@
# Active CRLH Transmission Line Modeler # Active CRLH Transmission Line Modeler
A MATLAB simulation of an **active Composite Right/Left-Handed (CRLH) transmission line** with a frequency-dependent negative resistance element. The structure achieves controlled gain across a user-defined passband by embedding an active shunt element (modeled as a negative resistance `Rn`) within a periodic CRLH unit cell topology. A MATLAB simulation of an **active Composite Right/Left-Handed (CRLH) transmission line** with a frequency-dependent negative resistance element. The structure achieves controlled gain across a user-defined passband by embedding an active shunt element (modeled as a negative resistance `Rn`) within a periodic CRLH unit cell topology.
This is supplemental code for the paper "Negative Resistance Enabled Amplifying CRLH Transmission Lines With Uniform Insertion Gain" (https://ieeexplore.ieee.org/document/11366944) This is supplemental code for the paper "Negative Resistance Enabled Amplifying CRLH Transmission Lines With Uniform Insertion Gain" DOI: 10.1109/LMWT.2026.3655243 (https://ieeexplore.ieee.org/document/11366944)
--- ---
## Background ## Background
@@ -29,7 +29,7 @@ The unit cell uses a ** symmetric T-network topology** with:
- Bloch impedance (real and imaginary) - Bloch impedance (real and imaginary)
- Outputs (in command window): - Outputs (in command window):
- Constituent CRLH parameters - Constituent CRLH parameters
- $R_n(\omega) exponential fit parameters - $R_n(\omega)$ exponential fit parameters
- $S_{21}$ at desired frequencies ($\omega_1$ and $\omega_2$) - $S_{21}$ at desired frequencies ($\omega_1$ and $\omega_2$)
- Maximum gain - Maximum gain
@@ -62,13 +62,22 @@ After cloning, add dependencies to your MATLAB path
## Design Equations ## Design Equations
CRLH element values are solved analytically from the two phase/frequency constraints: CRLH element values are solved analytically from the two phase/frequency constraints in Reference [1].
$$L_R = \frac{Z_0(\theta_1 \frac{\omega_1}{\omega_2} - \theta_2)}{n\,\omega_2\!\left(1 - \left(\frac{\omega_1}{\omega_2}\right)^2\right)}$$ Then, the required $R_n(\omega)$ is calculated as:
$$C_R = \frac{\theta_1 \frac{\omega_1}{\omega_2} - \theta_2}{n\,\omega_2 Z_0\!\left(1 - \left(\frac{\omega_1}{\omega_2}\right)^2\right)}$$ $$R_n(\omega) = -R_0e^{\alpha\omega}$$
with symmetric expressions for `LL` and `CL`. with
$$\alpha = \frac{\ln{\left(\frac{R_n(\omega_1)}{R_n(\omega_2)}\right)}}{\omega_1 - \omega_2}$$,
$$R_0 = -R_n(\omega_1)e^{-\alpha \omega_1}$$.
This will approximately fit the exact solution of:
$$R_n(\omega) = \frac{1 \pm \sqrt{1 - 4(G'_{sh} \omega L_L)^2}}{2G'_{sh}}$$
The required negative resistance at each frequency satisfies: The required negative resistance at each frequency satisfies: