Active Microwave Negative-Index Metamaterial Transmission Line with Gain

We studied the active metamaterial transmission line at microwave frequency. The active composite right-handed or left-handed transmission line was designed to incorporate a germanium tunnel diode with a negative differential resistance property as the gain device at the unit cell level. Measurements of the fabricated planar transmission line structures with one-, two-, and three-unit cells showed that the addition of the dc pumped tunnel diodes not only provided gain but also maintained the left handedness of the transmission line metamaterial. Simulation results agree well with experimental observation. This work demonstrated that negative index material can be obtained with a net gain when an external source is incorporated.

Figure 1

(a) Equivalent circuit model of a unit cell of a general metamaterial CRLH TL (active scenario: negative $R$ and/or negative $G$). (b) Schematic of a designed active CRLH TL unit cell in microstrip configuration. The dimensions are $a=2.5\mathrm{mm}$, $d=1.5\mathrm{mm}$, $l=9.7\mathrm{mm}$, $w=1\mathrm{mm}$, $s=0.2\mathrm{mm}$, $l_s=5.9\mathrm{mm}$, $r=0.3\mathrm{mm}$. (c) Current-voltage relation ($I\mathrm{\text{−}}V$ curve) of the germanium tunnel diode used in the active CRLH TL unit cell design. (d) Photo of a fabricated single unit cell of the active CRLH TL.

Figure 2

Measured transmission (scattering parameter $S_{21}$) magnitudes of the active CRLH TLs incorporating tunnel diodes: (a) one-unit cell, (b) two-unit cells, (c) three-unit cells.

Figure 3

Simulated (a) and measured (b) propagation constants of the active CRLH TL incorporating tunnel diodes with one-, two-, and three-unit cells. (c) Extracted index of refraction from the measured one-unit cell results [note that the positive $\mathrm{Im}(n)$ means gain with the convention used here].

Figure 4

Measured output power of the single-cell active CRLH TL circuit at the fundamental (2 GHz, blue circles), second (4 GHz, green crosses), and third (6 GHz, red triangles) harmonics as a function of the input signal power (in the NIM with gain region). The $\mathrm{\text{slope}}=1$ line (black line) is also plotted as a reference.