1. Microwave Amplifier Design

2. Power Gain Equation
Source Mismatch factor:
Load Mismatch factor:

3. . . . Power Gain Equation Example: In this system
Determine GA, GT, GP if:
Calculate PL, PAVN, PIN, PAVS if:
Calculate VSWRin, VSWRout
Solution: . . .

4. Power Gain Equation
Solution (cont.):
Using:
Using: . .

5. Stability Conditions
Stability condition of an amplifier is very important.
If an amplifier is not stable may be oscillated.
Stability can be determine by 1: [S], 2: matching networks 3: load
Oscillation are possible when input or output port presents a negative resistance:
For an unilateral device (S12=0), oscillation condition occurs when:
Unconditionally Stability:
Re{Zin}>0 & Re{Zout}>0 for all ZL & Zs or:
For a passive device, the real part of impedance is positive.
Otherwise for non-passive devices, network is potentially unstable for some ZL & Zs
equally:
Because: Γin=S11, 𝛤out=S22
For passive Zin & Zout is valid
is true for passive ZL & Zs 1 2 3 4

6. |ΓL-𝐶L|=𝑟L Stability Conditions Desired 𝜞L for stability
Stability Circles:
Where:
Using:
is center
is radius
|ΓL-𝐶L|=𝑟L
For:
For:
Desired 𝜞L for stability
Attention:

7. |Γs-𝐶s|=𝑟s Stability Conditions Desired 𝜞𝒔 for stability
Stability Circles (cont.):
As a similar manner:
Where:
is radius
|Γs-𝐶s|=𝑟s
is center
Desired 𝜞𝒔 for stability

8. Stability Conditions Unconditionally Stability:
Another Equivalent formula is:
Using:
Equivalent
Relation
is:
Where:

9. Stability Conditions Example:
S parameters of a BJT, at 15V, 15mA, is listed in table.
Draw stability circles.
Solution:
At 500MHz:
Stability circles:
At 1GHz:
At 2GHz:
At 4GHz:
Using:

10. Stability Conditions
Stability Circles:

11. Stability Conditions
A potentially unstable transistor can be unconditionally stable by a resistance or feedback.
Example:
S parameters of a BJT, at 800MHz:
Solution:
Using a series resistor in input:

12. Stability Conditions Other configuration: For input stability:
For output stability:
Adding resistance degrade gain, NF, VSWR.
Task-LN05-01: Delivery
Calculate new [S] for four configuration.
Show stability circle in ADS.
Is it unconditionally stable?

13. Constant Gain Circles Unilaterally Case: Maximum of GTU occurs if:
In this case:

14. Constant Gain Circles In unconditionally stable case:
Γi that produce a constant gain Gi presents a constant gain circle.
Normalized gain factor:
When Γi=S*ii , gain gi=1 & radius ri=0 as expected for Gi=Gmax
Example:
For given [S] of a BIJ at VCE=10V, Ic=30mA, f=1GHz
Determine Optimum terminations.
Determine GS,max, GL,max, GTU,max.
Draw several constant gain circle.
Design input matching for Gs=2dB
each value gi generates a circle

15. Constant Gain Circles Solution: Optimum terminations: Since
We draw circles:

16. Constant Gain Circles In potentially unstable case: Example:
For a FET having:
Draw circle Gs=5dB & 3dB.

17. Constant Gain Circles Simultaneous conjugate match: To max GT:
Solving Simultaneously these equations:
Γs & ΓL can be obtained namely ΓMS & ΓML as:
Minus sign is used for unconditionally stable.
In this condition (Simultaneous conjugate match):
Where:
Using:

18. Constant Gain Circles
Maximum stable gain is defined as GT,max when K=1:
Example:
Design a microwave amplifier using a GaAs FET to f=6GHz with maximum transducer gain.
Transistor at VDS=4V, IDS=0.5IDSS has [S]:
Solution:
Therefore:
FET is unconditionally stable
FET is not unilateral
Using:

19. Constant Gain Circles
Example (cont.):
Input Matching Network:
ΓMS

20. Constant Gain Circles ΓML Example (cont.): Output Matching Network:
In this example matching is designed for maximum of gain.
For optimum noise figure (NF), the design must be changed.
ΓML

21. Operating Power Gain
When S12≠0, operating power gain is used to design amplifier.
Operating power gain is independent of source impedance.
Unconditionally stable Case:
In appendix G the values of ΓL to draw constant operating power gain circles is presented.
The maximum of operating power gain occurs at:
Solution for Unconditionally stable is: =
Where:

22. Operating Power Gain Example:
Design a microwave amplifier using a GaAs FET to f=6GHz with operating power gain Gp=9dB.
[S] of transistor at Vds=4V, Ids=0.5IDSS :
Solution:
Circle of ΓL for 9dB gain is:
Typical ΓL is located in A:

23. Operating Power Gain
Solution (cont.):
Using CH2:
VSWRin=1 &

24. Operating Power Gain Potentially stable bilateral case:
Procedure for given Gp:
1. Draw operating power circles and output stable circle.
2. Select ΓL in power circle & stable region & not too close from stable circle.
3. Determine:
4. Draw input stable circle & determine if Γs=Γ*in lies in input stable region.
5. If Γs=Γ*in is not in stable region or is in stable region but is very close to stable circle, the value Γs or GP can be changed.
Example:
[S] parameter a microwave amplifier using a GaAs FET for f=8GHz, VDS=5V, IDS=0.5IDSS, IDSS=10mA is:
Solution:
FET is potentially stable in f=8GHz with:
Output stable circle:
Input stable circle:

25. Operating Power Gain Example (cont.):
Selected arbitrary ΓL in point A:
For conjugate match in input:
Using Γs:
Output is significantly mismatch.
To improve VSWR the locate Γs & ΓL must be changed.
Using:

26. Operating Power Gain
Example (cont.):
Other circles:

27. Available Power Gain Unconditionally stable Case (S12≠0):
Very similar previous section, available power gain can be obtained as:
For Potentially Stable Case (S12≠0):
1. For given GA, draw circles & input stability circle.
2. Select a value of Γs in stable region and not too close stability circle.
3. Calculate Γout & determine a conjugate match in output if feasible.
4. If ΓL=Γ*out is not in stable region or in stable region but is very close to it, ΓL or GA can be changed to arbitrary values.
A question:
Why ΓL should not be close to stable circle?
Where:

28. = ΓL Γb Γout VSWR Circles or Input VSWR:
Proof this using CH2
Input VSWR:
For constant VSWR (constant Γa), Γs circles should be plotted:
To VSWR=1:
Therefore we have:
By a similar way:
Where: or =
Γout Γb ΓL
Where:

29. VSWR Circles Example: [S] GaAs-FET at 12GHz, VDS=3.5V, IDS=25mA are:
Determine GA,max and draw GA= GA,max-1 dB circle.
Select several values Γs in this circle.
For each Γs value, determine ΓL in (VSWR)out =1.5 circles and draw this circles.
Select several values ΓL on (VSWR)out =1.5 circle. For each ΓL value, determine (VSWR)in.
Solution:
This example can be used to design low noise amplifiers (LNA) outlined in CH4.
For LNA we make trade-offs between Gain, NF, VSWR.
Constant circle for:
is unconditionally stable

30. VSWR Circles Γs values on circle: Four values presented in circle are:
For output VSWR=1.5:
Four circles are:

31. VSWR Circles Plotting four output VSWR=1.5:
In addition for values of VSWR=1 is plotted:

32. VSWR Circles Value ΓL in VSWR=1.5 is given as:
Results are listed in table as:
Task-LN05-02: Delivery
Do problem 3.30.
Plots circles in ADS.

33. VSWR Circles
Mapping:
ΓL & Γin as well as Γs & Γout are related by bilinear transformation as:
Therefore circles in Γin plane map into circles in ΓL plane.
Also, circles in Γs plane map into circles in Γout plane.
As presented in:
Circles of ΓL :
ΓL in Γs=Γ*in plane can be presented as:
As a similar way, Circles of Γs :
Γs in ΓL=Γ*out plane can be presented as:
Example:
[S] GaAs-FET at 4GHz, VDS=2V, IDS=25mA are:
Show GP, VSWR, stability.
Where:
Where:

34. VSWR Circles Solution: We select desired value of GP under GMSG as:
Constant gain circles:
In this circle, we select locations of:
is potentially unstable
For 2 points:
&

35. VSWR Circles
Other circle:

36. DC Bias Networks Two major biasing network is categorized as:
BJT Bias Networks
GaAs FET Bias Networks
BJT Bias Networks:
At microwave frequency ICBO, hFE, VBE are affected by temperature.
Typical reverse current:
Stability factors is defined as:

37. DC Bias Networks Two grounded emitter DC bias networks are: Example:
Design the DC bias of (b) type.
Assume that:
Solution:
Assuming Vbb=2 & IBB=1mA:
(a)

38. DC Bias Networks
At lower frequency a bypassed emitter resistor can be used for better stability.
Stability factors are:
A active DC bias network as shown:
Q1 stabilize operating point RF transistor as:
If IC2 tends to increase, I3 increases and then VBE,Q1 drops.
Therefore IB2 & IC2 drop and stabilized.
Where:

39. DC Bias Networks Selection DC point depends on the application.
Point A: for LNA & low power applications.
Point B: for LNA & high gains.
Point C: for high output power in class A
Point D: for higher output power and high efficiency in AB & B Class.
Example:
If HFE=100, VBE=0.7V, VCC=15V,
1. design a DC bias for previous figure to have VCE=8V & IC=2mA.
2. use active bias network and repeat solution.
Solution:
1. Dropping 10%VCC on RE:
2. I3=IC1+IC2 & IC1=IC2 :

40. DC Bias Networks GaAs FET Bias Networks:
Applications:
GaAs FET Bias Networks:
Can be bias using unipolar or bipolar networks as:
Apply VG then VD
Apply VG then VD
Apply VG then VD
is very important
Applications:

41. DC Bias Networks
Power supply sequencer:

42. DC Bias Networks Selection DC point depends on the application of FET.
Point A: for LNA & low power applications.
Point B: for LNA & high gains.
Point C: for high output power in class A
Point D: for higher output power and high efficiency in AB & B Class.
Active Bias Network:
Task-LN05-03: Delivery
Do problems
3.3
3.7
3.12
3.17
3.22
for a LNA biasing design