Microwave Amplifier Design Blog by Ben ( Uram ) Han and Nemuel Magno Group 14

1. Microwave Amplifier Design Blogby Ben (Uram) Han and NemuelMagnoGroup 14 ENEL 434 – Electronics 2 Assignment 2012

2. Specifications Bandwidth is defined as the narrower of the gain or input and output reflection coefficient bandwidths, where the gain bandwidth is determined by the 1dB points in the gain response, and the reflection coefficient bandwidth I where it is less than -10dB.

3. Microstrip Calculations We want to match the characteristic impedance of the microstrip to the connecting cables, i.e. 50Ω. We are given the measured dielectric constant (4.38), the PCB height (1.6mm), and the microstrip material and thickness (copper, 0.038mm). Using Txlineto calculate the width of microstrip required we get: For a 50Ω copper track, the width is 3.025mm. The wavelength is 153.3mm.

4. Emitter Degeneration 1 In order to improve the stability of the amplifier at low RF frequencies a resistance will be placed between the emitter and the ground, providing negative feedback and stopping oscillation. At our center frequency however we want to reduce emitter degeneration to improve gain. The emitter bypass capacitor will be connected in parallel to the emitter resistor and should provide a low impedance path to ground for the RF signal at the target frequency. Ideally we would set the series resonance frequency of the capacitor to match our center frequency. At 1075MHz the capacitor datasheet indicates that the capacitance should be ~20pF. This seems quite small compared to the collector capacitance of the transistor (~1pF). We will try a 100pF capacitor as an emitter bypass.

5. Emitter Degeneration 2 To calculate the value of the emitter resistor we will use an approximate value based on the collector current that we would like at bias point. From the BFR92A datasheet we see that at our center frequency of 1075MHz, the maximum stable gain is reached at ~13mA and the maximum unilateral power gain peaks at roughly the same point. Hence we will design to a collector bias current of 13mA. We will set the VCE bias at half the supply voltage, This should allow for adequate voltage swing of the output.

6. Bias Calculations 1 Using an approximate value for the collector resistor to start with we will choose 100Ω. For a collector bias current of 13mA the voltage drop across RE is: Using the approximation IC= IE we can calculate a value for RC given the VCE bias of 6V. We will use the nearest E24 series value of 360Ω. We will be using a voltage divider to bias the base (VB) so that the circuit is independent of β. Given and assuming Vbe is ~0.7V we get: In order to justify the assumption that VBis independent of β we need IB<< I2 = VB/R2. From the datasheet βtypical = 90.

7. Bias Calculations 2 Continued from last slide: So we want I2 much larger, say 10 times: Pick from the E24 range, say 150Ω, then R1= 5R2 = 750Ω. Simulation using RE = 100Ω, CE=100pF, R1= 750Ω, R2= 150Ω, RC= 360Ω, results in the following bias condition: Which shows that the assumption Vbe = 0.7V was slightly low, hence IC is also slightly lower. Tweaking the value of R2 to 160Ω gives the better result below, so we will use that instead.

8. Active 2-port Schematic The schematic below shows the transistor and emitter degeneration (plus the DC biasing) which was simulated to obtain the S-parameters.

9. Active 2-port Circuit Layout Below is a layout diagram showing the physical layout of the active 2-port section of the circuit (without the DC bias components, they will be included later).

10. Active Device K-factor and Maximum Gain Since we have |S11| < 1 and |S22| < 1, we just need K>1 for unconditional stability. We can see from the graph below that the amplifier is unconditionally stable above 369MHz. The maximum gain available at the target frequency is 9.907dB.

11. S-parameters 1 From simulation of active 2-port in MWO, we get the following graphs. We will use these S-parameter values in our design calculations.

12. S-parameters 2 Using Microwave Office to simulate the DC bias conditions, the S parameters of the active two-port amplifier are read from the output graphs and are listed below: Using the equations given in Pozar Ch.12, the required values for ГS and ГL to achieve simultaneous conjugate matching are: ГS= 0.1081/174.2 °ГL = 0.6696/22.63° (Calculations and working are shown on the next slide) So we need to design matching networks using Smith charts to convert the 50Ω generator and load, to ГS and ГL respectively.

13. Simultaneous Conjugate Matching Calculations The quadratic from conjugate matching provides two solutions. We want the reflection coefficient with an absolute value of less than 1. The other solution lies outside the Smith chart and indicates a negative resistance.

14. Matching Network (load end) Г2 = ГL* = 0.669/-22.6° yn = 1 + j1.8 ystub= -j1.8 d = 0.183 – 0.0315 = 0.1515 λ = 0.337 – 0.25 = 0.087 λ S/C b=-1.8

15. Matching Network(source end) Г1 = ГS* = 0.108/-174° yn= 1 + j0.23 ystub= -j0.23 d = 0.5 – 0.242 + 0.134 = 0.392 λ = 0.464 – 0.25 = 0.214λ b=-0.23

16. Simulation of matching networks made up with ideal transmission lines. Port 2 is used to provide a 50Ω termination in place of the generator or the load. ГS ГL The simulation results confirm matching networks provide the expected reflection coefficients small errors (due to graphical errors when using Smith charts)

17. Checking the design calculation for the simultaneous conjugate matching. The value for Г1 is slightly out. We will try to correct this with fine tuning when the matching networks are implemented with microstrips. Г1 ГL ГS Г2

18. Completing the circuit using the ideal transmission line matching networks gives the results shown in the graph below. The gain is acceptable at our center frequency and the reflection coefficients are at their minimum. This shows our calculations were valid.

19. Amplifier Test using Microstriplines 1 ГS Ideal transmission linesare replaced with microstrips and Port-2 provides the 50 ohm termination

20. Amplifier Test using Microstriplines 2 ГL Ideal transmission linesare replaced with microstrips and Port-2 provides the 50 ohm termination

21. Amplifier Test after Fine Tuning – Input After Fine Tuning In this section a T-junction discontinuity model has been added. The amplifier has also been fine-tuned so that ГSreflects the desired calculated value more closely (at least in simulations). Ideally: ГS = 0.1081/174.2 °

22. Amplifier Test after Fine Tuning – Output After Fine Tuning Again fine-tuning has been used to adjust the lengths of microstrip to achieve a closer match to the calculated value of desired ГL. Ideally: ГL = 0.6696/22.63°

23. Matching Network and Layout 1 ГL ГS These are the layouts associated with each matching network. ГL ГS

24. Amplifier characteristics with microstrip matching networks and ideal bias feeding network The bandwidth is limited by the -10dB point of the output reflection coefficient on the lower bound and the -1dB gain point on the upper bound. This gives a BW of 16.3%

25. RF Short Circuit Stub Termination 1 The value for the capacitor used to short the RF signal to ground at the end of the stub needs to be chosen to be resonant with its parasitic inductance to ensure a good connection to ground. However the impedance is significant for lower frequencies which may cause the signal to leak into the bias circuit. To resolve this situation we will add a second larger capacitor in parallel.

26. RF Short Circuit Stub Termination 2 The resistor is necessary to avoid parallel resonance between the two capacitors. The setup shown has better characteristics across the frequency range of interest.