Example 3: Two-stage Power Amplifier

As a third example, we consider the small-signal stability analysis of an X-band PA designed in the $0.25\mathrm{\mu m}$ GaN HEMT technology GH25-10 of UMS [10]. The circuit and its design are described in great detail in [30]. The resulting MMIC is shown in Figure E3.1.

The PA is a two-stage design where the second stage consists of two branches with each two transistors in parallel. In simulation, the second stage of the PA demonstrated an odd-mode instability [30], so a stabilisation resistor was added between the drains of the top and bottom halves of the second stage of the PA (as indicated in the figure).

The simulation of the complete PA was performed in ADS. The passive structures in the circuit were simulated with EM simulations in Momentum and combined with the non-linear transistor models afterwards. To verify the stability of the amplifier, the circuit impedance was determined at the gate of the top most transistor of the second stage.

The obtained impedance for $R_{\mathrm{stab}}=500\Omega$ is shown in Figure E3.2. The impedance is simulated on 945 logarithmically spaced points between $1\mathrm{MHz}$ and $50\mathrm{GHz}$. Because $1\mathrm{MHz}$ is not sufficiently close to DC, a bandpass filter was used in the stability analysis. Due to the low amount of data points in the resonances of the circuit, a Padé interpolation was used in the stability analysis. The resulting stable and unstable parts are shown in blue and red on the same figure. It is clear that the circuit is unstable for $R_{\mathrm{stab}}=500\Omega$. The unstable part peaks around $9.5\mathrm{GHz}$ and lies about $40 \mathrm{dB}$ above the interpolation error level.

The odd-mode instability can be resolved by decreasing the resistance of $R_{\mathrm{stab}}$ [30]. In a second stability analysis, we determined the stability of the PA for $R_{\mathrm{stab}}=25\Omega$. The results of this second analysis are shown in Figure E3.3. The obtained unstable part coincides with the level of the interpolation error, which indicates that the circuit is now stable.

Figure E3.1 Microphotograph of the MMIC. The stabilisation resistor $R_{\mathrm{stab}}$ is indicated in red.

Figure E3.2 Impedance seen at the gate of the first stage of the PA for $R_{\mathrm{stab}}=500\Omega$. Its obtained stable and unstable parts clearly indicate that the DC solution of the amplifier is unstable. The interpolation error (black -) is quite high due to the low amount of simulation points.

Figure E3.3 Impedance presented by the PA at the gate of the transistor in the first stage for $R_{\mathrm{stab}}=25\Omega$. The obtained stable and unstable parts indicate that the DC solution is now stable. The interpolation error is shown with (black -).