Amplifier Stability at High Frequencies and Stray Capacitance
Amplifiers are one of those critical components that make modern life possible. From wireless communication to power electronics, amplifiers need to run stably and predictably for these products to work properly. Stability analysis is one of my favorite topics in physics and engineering, and it always tends to crop up in places you would least expect. One of these places is in amplifiers.
Any time-dependent physical system with feedback and gain has conditions under which the system will reach stable behavior. Amplifier stability extends these concepts to amplifiers, where the system output can grow to an undesired saturated state due to unintended feedback. If you use the right design and simulation tools, you can easily account for potential instability in your circuit models before you create your layout.
How Stray Capacitance Affects RF Amplifier Stability
The source of instability in amplifier circuits, and between the input and output ports of an amplifier IC, is parasitic capacitance. This parasitic capacitance exists between the traces connecting to an amplifier. Parasitic capacitance is critical for setting the impedance of long traces (i.e., transmission lines) at a specific value. However, parasitic capacitance also provides an unintended path for feedback between the output and input ports.
Since this feedback path is capacitive, its impedance is lower when the input/output signal frequency is higher. These days, this is normally addressed at the chip level, but the contribution from PCB traces and pads will become more important as more RF amplifiers are running at increasingly higher frequencies. As little as a few pF of parasitic capacitance is enough to drive an amplifier to instability during operation.
At the board level, the stray capacitance at the input has a bandwidth limiting effect, where the bandwidth is reduced by a factor (1 + Gain). The solution is to design traces and pads at the amplifier ports to have minimal parasitic capacitance, or to add some compensating capacitance into the feedback loop. In the high GHz regime (e.g., mmWave frequencies), the spacing between components is larger than the critical length, so you would have to use impedance controlled routing. Integration of some components into SoCs is helping to eliminate this problem, but many RF amplifiers for upcoming devices are still packaged as individual components. A prime example is newer power amplifiers for mmWave applications.
The typical way to evaluate amplifier stability is to use the manufacturer’s evaluation board and measure any transient behavior directly. The other option is to determine the parasitic capacitance on the input and output traces connected to the amplifier and include these in a simulation. These simulations also allow you to experiment with a compensating capacitor on the amplifier’s feedback loop to counteract the parasitic capacitance.
How to Account for Stray Capacitance in a Simulation
Your schematic is just a 2D drawing of a perfect circuit. It does not contain any stray capacitive elements anywhere in your system and does not accurately reflect the real behavior of a PCB. That being said, the right design tools will make it easy to include parasitics in your PCB. Whether you are trying to simulate self-resonances in passives, or you want to simulate stray capacitance in other portions of your system, you’ll need to add capacitors to your schematic in strategic locations.
To simulate stray capacitance at the input to an amplifier, simply add the right size capacitors and an AC source to your amplifier input. The capacitors are placed as shunt elements (i.e., connected to the common ground connection) on the input and the output ports of the amplifier. You’ll also need to use a verified component model for your amplifier component to get a feel for the amplifier’s behavior in the presence of parasitic capacitance. The shunt capacitive elements will model coupling between ground and the input/output traces in your board.
Expected Transient Analysis Results
With transient analysis, you can see whether the signal becomes unstable and grows to saturation over time as the amplifier runs. The graph below shows some example results for a 100 GHz signal with strong instability due to large parasitic capacitance. Here, the transient voltage at the output reaches a saturation value of 2 V due to unintended strong feedback and a high-input signal level.
Note that losses have not been considered in the above feedback example, and it is known that loss in the substrate may cause an otherwise unstable device to become stable as this compensates for gain in the unintended feedback loop.
Expected Pole-Zero Analysis Results
In the pole-zero analysis results, you would expect to see two poles in the simulation outputs. One would be a stable pole, representing the stable feedback loop. The eigenvalue for this pole would have a negative real part. If the circuit is unstable, another pole should appear as a second eigenvalue with positive real part; this corresponds to an unstable growing oscillation due to feedback via parasitic capacitance. You can see some example pole-zero analysis results on this page.
There is another type of stability corresponding to a damped stable oscillation, also known as a limit cycle. This decaying transient can result in stable oscillating behavior, similar to what is seen in amplifiers used in differentiator configuration without a series resistor on the input. You can identify this behavior from pole-zero analysis results by comparing the damping constant (the real part of an eigenvalue) with the transient oscillation frequency.
The advanced PCB design and simulation features in Altium Designer® allow you to perform a variety of analog simulations for your next RF system and amplifier circuit. You’ll have a number of tools to assess amplifier stability as part of circuit design and analysis. Once you’re ready to plan your layout, you’ll have a set of tools to capture your schematic and start creating high quality layouts.