Example 2: Balanced amplifier

The second example is a balanced amplifier built as a student project for operation around $3.4 \mathrm{GHz}$ (Figure E2.1). Two BFP520 transistors were used to construct the amplifier. During measurement, the design oscillated around $1.43 \mathrm{GHz}$ when terminated with $50 \mathrm{\Omega}$, so the circuit is a good candidate to verify the proposed method to find the instability in simulations.

The small-signal current source was connected to the collector of the top transistor. The BFP520 has a $f_{\mathrm{T}}$ of $45 \mathrm{GHz}$, so the maximum frequency for the simulation was set to $50 \mathrm{GHz}$. The impedance of the circuit was determined starting from DC in $10 \mathrm{MHz}$ steps. The obtained impedance is shown in green in Figure E2.2, the obtained stable and unstable parts are also shown in the same figure. The instability around $1.46 \mathrm{GHz}$ is detected, but also some artefacts can be observed in the obtained unstable part at higher frequencies. The high level of the interpolation error at the frequency of these artefacts indicates that they are due to the interpolation in step 3 of the stable/unstable projection. At the frequency of the detected instability, the unstable part lies about $30 \mathrm{dB}$ above the error level, which indicates that the instability is not an interpolation artefact.

To confirm that the artefacts are caused by the interpolation, a second simulation was run, but now $1 \mathrm{MHz}$ steps were used instead of $10 \mathrm{MHz}$. The stable/unstable projection of the denser frequency response data (Figure E2.2) still predicts the instability around $1.46 \mathrm{GHz}$, but the artefacts in the unstable part at higher frequencies are gone. The maximum of the interpolation error went down to $-80 \mathrm{dB(\Omega)}$.

Figure E2.1 Simulation set-up and photograph of the balanced amplifier. In the simulations for the stability analysis, the amplifier is excited at the collector of one of its transistors. All transmission lines in the circuit are $50\Omega$ lines unless stated otherwise. The length of the transmission lines is given in millimetres. The TLINP model was used for the transmission lines with $\epsilon_{r}=6.15$, $\tan(\delta)=0.003$ and conductor losses $A=2.5 \frac{\mathrm{dB}}{\mathrm{m}}$.

Figure E2.2 The separation of the impedance (green -) into the stable part (blue -) and unstable part (red -) reveals the instability around $1.46 \mathrm{GHz}$. The interpolation error is shown with (black -). In the plot on the top, there are artefacts present in the unstable part due to interpolation of the coarsely obtained impedance data. When the impedance of the balanced amplifier is simulated on a finer frequency grid, the artefacts disappear (bottom).