Modeling Class E/F RF Amplifiers, Part 2

[Part 1 can be found here] 

In Part 1 I evaluated a Class E/F amplifier using a center-tapped transformer to supply power to the drains of the two active devices. 

DC power can also be fed to the drains of the two MOSFETs via two inductors, thus simplifying the transformer because it no longer needs to be center-tapped. I was curious how such a circuit compared (in performance) to the circuit described in Part 1. 

Here's the SPICE model (using Linear Technology's free SPICE program: LTSpice):

   

(Click on image to enlarge)

Regarding the model: 

1. C4, at 1 Farad, provides a "stiff" AC ground for simulation purposes so that there's no voltage fluctuation at the R4, C4, L1, L2 node. 

2. L1 and L2 provide a high-impedance feed for DC power to the "Drains" of the MOSFETs. I chose these to be (initially) 25 uH. 

3. The MOSFETs are modeled with voltage-controlled switches. Their Ron is set via external resistors to be 0.15 Ω (plus 0.01 Ω within the Switch model). 

4. 500 pf capacitors mimic the MOSFETs' C_oss (per the IRF 530 datasheet). Note that these capacitors are not voltage dependent. 

5. Refer to Part 1 for more detail on selecting the Transformer inductance of 400 nH. 

6. C3 was arrived at by trial-and-error (after initially setting its value to 3.655 nF per Part 1) by adjusting its value so that the voltage waveform at node "Va" is zero when the current waveform (through R1) is non-zero.

    

(Click on image to enlarge)

When adjust the value of C3 (or the transformer's inductance), the current and voltage waveforms maintain the same relationship to C3's value (or to the transformer's inductance) as was described in Part 1. Refer to the image below.

   

(Click on image to enlarge)

Lowering RMS current through the switches: 

I thought I'd see if I could lower power dissipation in the switching devices by lowering their RMS current (see Part 1 for more discussion on this technique). By lowering the value of inductance of L1 and L2, I could replicate current waveforms through the switching devices that look as though the amplifier is now a a "Class E/F_2,odd" amplifier, but, when I made my measurements using the tools in LTSpice, there was really only minimal effect (if any) in power dissipation. 

Here's how the waveforms look with L1 and L2 reduced to 800 nH. As the table following this image shows, although the current-waveform changes significantly, there isn't much of a difference in switching-device power-dissipation (as measured across R1 and R2).

   

(Click on image to enlarge)

I used the LTSpice measurement functions to measure power and RMS current at different points in the circuit (for various values of L1, L2), and these measurements have been tabulated below.

   

(Click on image to enlarge)

Some observations from this table:

• I really cannot see much change in R1's power dissipation as L1, L2 are varied. That is, the differences are small, and perhaps are within the tolerance of simulation errors.
• Also, there's not much change in either Output Power (Pload) or efficiency for the range of values of L1 and L2 shown in the table. Therefore, a L1, L2 values in the range of, say, 25 uH - 100 uH, might be the simplest approach for my application.
• As L1, L2 are decreased, C3 must be increased to compensate for their effect on the time-relationship of the voltage and current waveforms. However, an increase in the value of C3 increases the current through C3 (because voltage across the transformer is essentially constant, and we decrease C3's reactive impedance when we increase its value). Therefore, due to its internal ESR, C3 will dissipate more power when L1,L2 are reduced.
• As the values of L1 and L2 is increased, it takes longer for the simulation waveforms to ramp up to their final values.

From the minimal change in R1 dissipation, and from the gross changes in C3 current (and thus, potentially, its power dissipation), it really doesn't make much sense (in my application) to attempt to "tune" L1 and L2 to minimize power dissipation in the switching devices by minimizing their RMS currents. 

It's possible, though, that in applications in which higher currents are present, some benefit might be achieved by "tuning" L1 and L2. However, the simulations don't bear this out in my application, and there seems to be little benefit. 

Overall, the power-out from this circuit topology is comparable to that of the center-tapped transformer topology described in Part 1. So, for my application, either circuit should do the job, and it'll just be a matter of determining which one is easiest to build. 

Modeling with the IRF530 MOSFET 

Actual MOSFETs can be simulated via LTSpice's "nmos" model, within which one can retrieve the SPICE parameters for a number of different MOSFETs, including the IRF530. (Note: these devices are not alphabetized in the "Pick New MOSFET" table.) 

Below is a circuit with IRF530 MOSFETs substituting for the original voltage-controlled switches. The final value of C3, as well as the AC source's amplitude and offset voltage (V2), were arrived at by trial-and-error. Also, two AC sources are used (the second with an offset of 180 degrees), because it seemed like an easy way to provide two sine-wave sources that were 180 degrees out of phase but with the same DC offset.

   

(Click on image to enlarge)

There are several differences between this circuit model and the original one with the voltage-controlled switches:

1. The Sine Wave sources have an amplitude of 10 Vpeak and a DC offset of 5V (to bias the IRF530's near their turn-on point). This gives peak gate voltages of +15/-5 Volts (note that the max rating of the IRF530's gate voltage (V_GS) is +/- 20V).
2. C3 is now 3.69 nF.

Here is the Drain Voltage versus Source Current for one of the IRF530 MOSFETs:

   

(Click on image to enlarge)

Note: Source current is shown, rather than Drain current, because the Drain pin has quite a bit of current flowing through it even when the MOSFET is OFF. This current at the Drain pin is not dissipative current, though (that is, it isn't being dissipated as I² * R heat through R_DS(on). Instead, it's current passing through the Gate-Drain capacitance and out the Gate pin (LTSpice plots verify that I(drain) - I(gate) = I(source)). 

Here are some of the currents and powers (and overall efficiency) measured via LTSpice.

• RF Power Out: 48.2 watts
• DC Power In: 52.0 watts
• Efficiency: η = 48.2/52.0 = 93%
• I_L1 = 1.14 A_RMS
• I_C3 = 4.5 A_RMS
• I_L3 = 5.2 A_RMS

Note the high currents in C3 and L3. Care should be taken to use low-ESR devices! 

References: 

Spice:

• Free Download of LTSpice here.
• LTSpice "Getting Started Guide" here.

Class E Amplifiers:

• Sokal, "Class-E RF Power Amplifier", Jan/Feb 2001, QEX
• Sokal, "Class-E High-Efficiency RF/Microwave Amplifiers", (a more detailed paper)
• Lau, Chiu, Qin, Davis, Potter, Rutledge, "High-Efficiency Class-E Power Amplifiers" Part 1, May '97, QST, and Part 2, June '97 QST
• Davis, Rutledge,"A Low-Cost Class-E Amplifier with Sine-Wave Drive"
• Der-Stepanians, Rutledge, "10-MHz Class-E PowerAmplifiers"
• Melia, Robert, O'Conner, Class-E Power Amplifier Design
• Tayloe, Class E Amplifiers (Norcal QRP Presentation)
• Class E Design Software from Tonne Software (I've never used this, so use at your own risk)
• WA0ITP Class-E Amplifier Design Spreadsheet (I've never used this, so use at your own risk)
• Class-E AM Forum
• Class-E AM Transmitters (WA1QIX)
• Class-E Amplifier Experiments , Calculations, and Notes on Designing Class-E RF Amplifiers, all by Bill Slade. (I've not verified the accuracy of these posts.)

Class E/F Amplifiers:

• Taniguchi, Potter, Rutledge, "A 200 W Power Amplifier", Jan/Feb 2004, QEX
• Letters, May/June 2004, QEX
• Letters, July/August 2004, QEX
• Kee, Aoki, Hajimiri, Rutledge, "The Class E/F Family of ZVS Amplifiers"
• Kee, "The Class E/F family of Harmonic-Tuned Switching Power Amplifiers" (Cal Tech Thesis)
• Kee, Aoki, Rutledge, "7.1 MHz, 1.1 KW Demonstration of the New E/F2,odd Switching Amplifier Class"
• Jeon, "Design and Stability Analysis Techniques for Switching Mode Non-Linear Circuits: Power Amplifiers and Oscillators" (Cal Tech Thesis)
• Kee, et al. U.S. Patent, No. 6,724,255
• Niknejad, "Class E/F Amplifiers" (presentation, EECS 242, U.C. Berkeley)
• Bohn, Kee, Hajimiri "Demonstration of a Switchless Class E/Fodd Dual-Band Power Amplifier (a 40 and 30 meter dual-band amp)

Caveats: 

1. These simulations are for educational purposes only. 

2. I could have easily have made a mistake, so please view (and use) these simulations accordingly.  

3. And a final caveat regarding SPICE modeling. Modeling results should always be taken with a bit of caution, for the ability of SPICE to mimic actual circuit behavior depends in large part on how accurately a circuit and its components have been modeled. Factors such as parasitic components and circuit non-linearities can all cause modeled SPICE performance to diverge from actual performance. SPICE can provide valuable insights into circuit operation, but a bit of skepticism, too, should be applied when evaluating results.