Parent Category: 2015 HFE

*By John E. Penn*

**Introduction:**

Most Radio Frequency (RF) and microwave engineers know about amplifier stability but may not understand odd mode stability. Computer Aided Design (CAD) tools have the standard stability measures including the single stability parameter mu^{1}, but these represent “even” mode stability. Often this is sufficient for most amplifier designs unless one is doing a balanced amplifier, or power amplifier, that is, anything that has more than one device in parallel. The purpose of this article is to explain odd mode stability and demonstrate it using the common RF CAD tools, Keysight’s Advanced Design System (ADS) and National Instruments/Applied Wave Research’s (NI/AWR) Microwave Office (MWO). Also, measured results are shown from an amplifier designed to demonstrate even and odd mode stability.

Often, the best way to learn RF and Microwave amplifier design is to build and test an actual circuit, not just perform a design based entirely on simulations. After all, a significant portion of a typical engineer’s time is spent figuring out why something is not working as expected. Simulations can only take one so far, actual measured performance is much more useful.

**Hands-On Experience**

Many Universities offer engineering courses with hands-on practical experience. Johns Hopkins University’s (JHU) Engineering for Professionals (EP) offers several classes that include hands-on practical experience. The author, John Penn, co-teaches one such class, RF & Microwaves II, with Dr. Willie Thompson. Students design a low noise amplifier and a medium power amplifier, then fabricate and test those circuits during one of the laboratory sessions. These designs typically are single stage amplifiers using a single layer Rogers RO4003 dielectric board, 0.06”x0.03” (0603) chip resistors, inductors, and capacitors, plus a Gallium Arsenide (GaAs) Pseudomorphic High Electron Mobility Transistor (PHEMT) in a plastic package, e.g., Avago atf54143 or atf34143.

During the course, students learn the different tradeoffs of amplifier design—gain, noise figure, output power, power efficiency, bandwidth, return loss, DC bias, and stability. Sometimes those amplifier designs oscillate unintentionally. Learning how to distinguish the type of oscillation, low frequency versus high frequency, and how to quell the oscillation is an important part of the student’s experience of building and testing their designs. When those amplifier designs do not work as expected, yet they are able to figure out and solve the problem—those hard earned lessons make a strong impression.

**Usual Solutions**

For high frequency oscillations, maybe the tradeoff of gain versus stability was too aggressive in the amplifier design which might be solved by modifying the stabilizing resistor values. Conversely, for low frequency oscillations—a few MHz, providing the appropriate capacitors on your DC bias flags is the likely solution. That 0603 100pf chip capacitor makes a nice RF short circuit at microwave frequencies, a few GHz, but does not isolate the external power supplies from the amplifier at a few MHz! The usual solution is multiple parallel capacitors on the bias flag to provide a nice RF short circuit from a few MHz to a few GHz. Usually, a 100pf 0603 chip capacitor in parallel with an 0.08”x0.05” (0805) 1uf chip capacitor solves the low frequency oscillation problem. Figure 1 shows a typical board layout with DC bias flags for gate and drain supplies, SMA connectors for the RF input and output, a 4 pin SOT343 Avago 34143 PHEMT, chip capacitors, and a chip resistor for stability.

**Figure 1 • Typical 2”x2” Medium Power Amplifier Design Layout (525.775).**

So, while many RF engineers understand stability, it is most often the even mode stability that they are familiar with. Another type of oscillation in amplifiers is odd mode oscillation, which does not occur in the single transistor designs. As is probably the case with most RF courses, students build and test single transistor amplifiers. Multi-stage amplifier stability and odd mode stability are not always covered in the basic RF courses. JHU students can take Professor Dale Dawson’s Power MMIC Design course to learn about odd mode oscillations, which can occur when you combine parallel transistors to increase output power. That class also teaches about subtle bias dependent, or non-linear, stability, not just small signal linear stability.

As a means of analyzing and demonstrating odd mode oscillations in an actual circuit, an amplifier was designed, built, and tested to illustrate this phenomena. This amplifier has the potential to oscillate in an odd mode as well as an even mode.

Predicting stable and non-stable operation with standard CAD tools, e.g., Keysight’s ADS and NI/AWR’s MWO, is discussed with comparison to the actual measured results. Figure 2 shows the layout of an amplifier using two parallel Avago 54143 PHEMTs, along with a series chip resistor to stabilize the even mode, and a shunt chip resistor on the outputs of the two transistors for stabilizing the odd mode.

**Figure 2 • 2" x 3" Odd Mode Power Amplifier Demo Design Layout (525.775).**

Non-linear models, as well as linear s2p files, were available for the Avago 54143 PHEMT, for both Keysight’s ADS and NI/AWR’s MWO programs. One technique to analyze odd mode oscillations uses a transient simulator and requires non-linear models for the transistor. Another odd mode analysis technique only requires a linear simulator and linear models, or s2p files, of the transistors. Both techniques are discussed in the course notes for Professor Dawson’s Power MMIC Class^{2}, and the students do a homework exercise to illustrate the first transient technique. Both approaches will be explained.

**Odd Mode Oscillation**

What is an odd mode oscillation? While the standard even mode stability approach analyzes the stability of the amplifier over any possible passive impedance applied to the RF input and output, an odd mode oscillation would occur if applying a short circuit applied at the microstrip “tee” intersection where the two gates, or two drains, of the PHEMTs in figure 2 causes an instability. The series and/or shunt resistors to the left of the tee that splits the input to the two PHEMTs affects even mode stability but will not affect odd mode stability. Conversely, the shunt resistor connected to the drains of the two PHEMTs has no effect on the “normal” even mode operation of the amplifier but can completely determine whether there will be an odd mode oscillation in the design.

**Figure 3 • Odd Mode Power Amplifier Two-Way Combiner Layout.**

It would be possible to prevent odd mode oscillations by making the upper branch and lower branch of the combined amplifier sections unconditionally stable by using series and/or shunt resistors on the gate of each PHEMT “before” the two branches are connected. If each branch were unconditionally stable, then the amplifier would be stable, even with that “virtual” short circuit of the odd mode. This demonstration amplifier was intentionally designed such that changing the shunt resistor at the drains of the PHEMT would cause a known odd mode oscillation, or could damp out the odd mode oscillation.

**Transient Odd Mode Analysis**

One method to look at odd mode stability is to do a transient analysis to determine if an oscillation will build—bad, or damp out—good. This requires both a transient simulator and a good non-linear model. For the demonstration circuit I used the Avago 54143 PHEMT since there was a non-linear model for both ADS and MWO, as well as s2p files at various DC biases. Figure 3 shows the arrangement of the two parallel devices with a shunt resistor at the drains for damping an odd mode stability. If there is an odd mode stability problem, the transient simulation should show a problem if there is no resistor between the two PHEMT outputs.

**Figure 4. MWO Schematic of Odd Mode Power Amplifier. **

Figure 4 shows the full schematic of the amplifier for demonstrating odd mode oscillation as entered in Microwave Office (MWO). Note the DC supplies which are required for proper operation of the non-linear model, as well as the addition of a simulation element to provide an impulse spike at one of the PHEMT outputs. If the circuit is stable, this impulse should attenuate, or damp out. Conversely, if it is unstable, the odd mode oscillation will build. Figure 5 shows the odd mode oscillation building when the odd mode stabilizing resistor is 5000Ω. Using the markers at two peaks predicts an oscillation frequency of about 1.04GHz (period=0.96ns). Note that the oscillation frequency is the odd mode oscillation frequency of each transistor, which are 180 degrees out of phase with each other. As will be shown in simulations and measurements, the difference of these two signals dominates the output which is at twice the frequency of oscillation. The transient simulator predicts that the impulse dampens out with a 100Ω odd mode stabilizing resistor (see figure 6).

**Figure 5 • Transient Simulation in MWO Schematic with a 5000Ω Odd Mode Resistor.**

**Figure 6 • Transient Simulation in MWO Schematic with a 100Ω Odd Mode Resistor.**

Similar results are achieved with ADS using its transient simulator. Figure 7 shows the full schematic of the amplifier for demonstrating odd mode oscillation in ADS. Likewise figure 8 shows the odd mode oscillation with a 5000Ω odd mode resistor, with a frequency of oscillation around 1.1 GHz. The sum of these two out of phase odd mode oscillations appears as a 2.2 GHz (2X) oscillation frequency at the combined output as shown in figure 9. When a 100Ω odd mode resistor is used, the oscillation does not occur, as shown in figure 10. Convergence with the transient simulator and a particular non-linear model can be difficult. One may have to modify some of the simulation options in ADS or MWO to achieve a successful transient simulation.

**Figure 7 • ADS Schematic of Odd Mode Power Amplifier. **

**Figure 8 • Transient Simulation in ADS Schematic with a 5000Ω Odd Mode Resistor.**

**Figure 9 • 2X Frequency of Oscillation at Output (Transient Simulation in ADS).**

**Figure 10 • Transient Simulation in ADS Schematic with a 100Ω Odd Mode Resistor.**

**Eigenvector Odd Mode Analysis**

Another method with similar results to the transient simulation only requires a linear model, or s2p files, of the devices^{3}. One only needs to simulate the portion of the schematic where a virtual short circuit at the point of symmetry of the 2-way combiner would cause an odd mode oscillation. If the real portion is negative and the phase is zero, oscillation can occur. This method may miss some potential oscillations where the oscillation is dependent on subtle non-linear operation of the device, but it will yield useful results when either a non-linear model is not available, or the transient simulator is not available, or when the transient simulation fails to converge.

Figure 11 shows the MWO schematics of the parallel combiner portion of the amplifier split into an input (2x54_FET_Part1_LambdaIn) and an output portion (2x54_FET_Part1_LambdaOut). The equations used to calculate odd mode stability in MWO are shown in figure 12. When the phase is zero, and the real portion is negative, the odd mode oscillation condition exists. Results are similar to the transient method, predicting an odd mode oscillation around 1 GHz with a high odd mode resistor value (fig. 13), while the odd mode is stable with a 100Ω resistor (fig. 14).

**Figure 11 • MWO Schematic of Input and Output for Eigenvalue Calculation.**

**Figure 12 • Equations to Calculate Odd Mode Stability using the Eigenvalues in MWO.**

**Figure 13 • MWO Plot Showing Odd Mode Oscillation with a 5000Ω Resistor. **

**Figure 14 • MWO Plot Showing Odd Mode Stability with a 100Ω Resistor.**

For ADS, the schematics are similar in terms of splitting an input and output portion of the parallel combined amplifier to calculate eigenvalues. Figure 15 shows the schematic of the output portion with an added block to calculate Z-parameters (Z=stoz(S,1)). This conversion element to get Z-parameters was included in both the input and output amplifier halves ADS schematics. The rest of the equations as shown in fig 16 were included in the data display block within ADS. Comparable plots using ADS showing odd mode oscillation at about 1.07 GHz with a 5000Ω resistor and a stable odd mode with a 100Ω resistor are shown in figures 17 and 18, respectively.

**Figure 15 • ADS Schematic of Output for Eigenvalue Calculation (Z=stoz(S,1)).**

**Figure 16 • Equations to Calculate Odd Mode Stability using the Eigenvalues in ADS.**

**Figure 17 • ADS Plot Showing Odd Mode Oscillation with a 5000Ω Resistor.**

**Figure 18 • ADS Plot Showing Odd Mode Stability with a 100Ω Resistor.**

**Measured Performance of Demonstration Amplifier**

The demonstration amplifier with two parallel 54143 PHEMTs was fabricated on 20 mil Rogers RO4003 material using 100pf chip capacitors for DC blocks and also for use in parallel with 1uF chip capacitors to isolate the Vgg and Vdd DC biases, plus a 20Ω chip series resistor at the input for even mode stability. Initially the odd mode resistor on the drains of the PHEMTs was not added. As expected the circuit oscillated as shown in the spectrum analyzer plot of figure 19. You can see the oscillation frequency of 1.3 GHz and its harmonics. The output of 2X the oscillation frequency at 2.6 GHz is particularly strong, as expected.

**Figure 19 • Spectrum of Amplifier Showing Odd Mode Oscillation (No Resistor).**

When a 100Ω odd mode chip resistor was installed, the amplifier was stable. At that point, s-parameters were measured and compared to the linear simulations (fig. 20). Note the good agreement once the amplifier is stabilized. Typical amplifier simulations will not show an odd mode oscillation problem, but it should be noted that the transient method can predict both even and odd mode oscillations. One difference in the spectrum between even and odd mode oscillations, is that an odd mode oscillation should have a very strong signal at 2X the oscillation frequency.

**Figure 20 • Measured versus Simulations of Stable Amplifier (100Ω Shunt Resistor).**

**Summary**

An amplifier was designed, built, and tested to illustrate odd versus even mode oscillations. Also shown were a couple of simulation techniques to predict odd mode oscillations. These techniques were illustrated using common RF CAD tools, e.g., Keysight’s ADS and NI/AWR’s MWO. Common stability parameters such as “mu” ^{1} only illustrate even mode stability, which is sufficient for single transistor amplifiers. But when one parallel combines transistor devices, odd mode oscillations can occur due to the “virtual” short circuit at the symmetry point of the combiner. Transient simulations requiring non-linear device models can be used to predict both even and odd mode oscillations. A simpler technique is to look at the eigenvalues which only requires a linear simulator and a linear model, or s2p file, of the transistor. Of course this may not catch subtle instabilities due to the non-linearities of the particular transistor. Both techniques were useful in predicting the actual odd mode oscillations of this demonstration amplifier design.

**About the Author**

John E. Penn received a B.E.E. from the Georgia Institute of Technology in 1980, an M.S. (EE) from Johns Hopkins University (JHU) in 1982, and a second M.S. (CS) from JHU in 1988. Since 1989, he has been a part-time professor at Johns Hopkins University where he teaches RF & Microwaves I & II, MMIC Design, and RFIC Design. Email: profpenn@gmail.com.

**References:**

1)Marion Lee Edwards and Jeffrey H. Sinsky, A new Criterion for Linear 2-Port Stability Using a Single Geometrically Derived Parameter, IEEE Transactions on Microwave Theory and Techniques, vol. 40, No.12, pp. 2303-2311, Dec. 1992

2)Professor Dale Dawson, Power MMIC Design Course Notes, JHU 525.788

3)Ron Freitag, A Unified Analysis of MMIC Power Amplifier Stability, IEEE MTT-S Digest 1992, pg 297-300