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IV. Microwave Amplifier Design 1. - Microwave Amplifier Specifications: Frequency range Power Gain Gain flatness Input voltage standing wave ratio VSWR Output voltage standing wave ratio VSWR Noise Figure NF Output Power at 1dB Gain Compression 2. - Amplifier Topologies (see next page) Reflective Match Amplifier Feedback Amplifier Balanced Amplifier Distributed Amplifier 3. - Reflective Match Technique For narrowband applications ( <10% bandwidth) Good input/output VSWR over the narrowband Best noise performance Stability problem at out-of-band frequencies and needs to be controlled in the design of matching networks 49 50 4. Microwave Small Signal Transistors Two commonly used categories of microwave transistors: i. Silicon Bipolar transistor (BJT) ii. Galium Arsenide Field Effect Transistors (GaAs FET) - Metal Semiconductor Field Effect Transistor (MESFET) - High Electron Mobility Transistor (HEMT) Comparison between BJT and GaAs FET i. For application below 4GHz, BJTs have several advantages: - It has a well established technology and hence lower cost & proven reliability. - Low noise BJTs generally operate with lower bias currents and lower figures. - BJTs are easier to match over a wide bandwidth and are normally unconditionally stable below 4GHz. - The optimum source impedance for low-noise operation of BJTs leads to a smaller trade-off between noise performance and gain. ii. Advantages of GaAs FET over BJTs - Can operate at even higher frequencies, higher than 10 GHz. - Higher gain & lower noise figure (HEMTs have the best noise performance). Transistor Packing Transistor packaging parasitic are significant at microwave frequency, in general i. Packaged transistors for narrowband design. ii. Unpackaged transistors (die form) for wideband and ultrawideband designs. 51 5. S-Parameters Like the other two-port network parameters such as y, z, h, or ABCD parameters, at high frequencies, we prefer to use the s parameters to characterize high frequency two-port networks, such as a high-frequency amplifier circuit. As shown in the figure below, the s-parameters are defined in terms of the incident and reflected power waves rather than the voltage and current, which are sometimes difficult to be defined at high frequencies. 1 2 Two-port network a1 b1 1' [ss ss ] 11 12 21 22 a2 b2 2' The s parameters are defined as: b1 s11a 1 s12a 2 b 2 s 21a 1 s 22a 2 where a1 = square root of the power incident at port 1 a2 = square root of the power incident at port 2 b1 = square root of the power reflected from port 1 b2 = square root of the power reflected from port 2 The reflection coefficient at a certain point in a circuit is defined as Z Z o square root of the power reflected Z Z o square root of the power incident where Z is the impedance at the point and Zo is the system impedance. In the above formula, Z can be the load impedance, the source impedance, the input impedance, or the output impedance. The corresponding reflection coefficient will then be called the load, the source, the input, and the output reflection coefficients, respectively. 52 6. Amplifier Power Gain Equations i. An amplifier circuit can be modeled as a two-port network as shown below. s is the source reflection coefficient and ℓ is the load reflection coefficient. One of the important parameters of the amplifier is the transducer power gain, which is defined as: Gt P Pavs where Pℓ the power delivered to the load and Pavs is the power available from the source. The S-parameters, s and ℓ all contribute to the transducer power gain. The transducer power gain can be expressed as: 2 Gt S21 1 2 1 2 s 1 S11 s 1 S22 S21s S12 2 53 Other forms of Gt are: Gt Gt where 1 s 1 in s 2 1 s 2 1 S11 s 2 in S11 out S22 S21 2 S21 1 2 2 1 S22 1 2 2 2 1 out 2 S12S21 1 S22 S12S21s 1 S11s ii. If S12 0 , it is called the unilateral case. Transducer power gain Gt 1 s 2 1 S11 s 2 S21 1 2 2 1 S22 2 Maximum unilateral transducer power gain can be obtained when S = S11* and ℓ = S22*. Because in S11 out S 22 S12S 21 1 S 22 S12S 21s 1 S11s 54 S11 S12 0 S 22 S12 0 therefore G tu,max S21 2 1 S 1 S 2 2 11 22 iii. If the two-port network is terminated in a Zo system, where S = 0 and ℓ =0, then Transducer power gain G t S21 2 iv. If the system is unconditionally stable, maximum transducer power gain happens when in = S* and out = ℓ*. The expression of the transducer power gain will be derived later. 55 Example: A GaAs MESFET has the following S-parameters measured with Vds =4V and Ids= 30mA at 8GHz with a 50 Ω reference. S11 = 0.55 158o S12 = 0.01 -5o S21 = 1.95 9o S22 = 0.46 -148o s = 0.20 0o ℓ = 0.33 0o Calculate the transducer power gain. Solution: The transducer power gain equation is 2 Gt S21 1 2 1 2 s 1 S11 s 1 S22 S21s S12 2 2 1.95 1 0.33 2 1 0.20 2 1 0.55 x 0.2158 1 0.46 148 x 0.33 0.01 5 x 1.959 x 0.20x 0.33 = 2.08 = 3.18dB 56 2 7. Amplifier Stability Consider an amplifier circuit shown below: The amplifier is unconditionally stable if in 1 and out 1 Using the above condition, stability circles which define graphically stable values of source and load reflection coefficients can be derived. 1. Output Stability Circle: 2. Input Stability Circle: values for in 1 s values for out 1 r c S12S21 2 S22 S radius 2 * * 22 S11 2 S22 2 rs center cs 57 S12S21 2 S11 S radius 2 * * 11 S 22 2 2 S11 center The input and output reflection coefficients are given by: in S11 S12S21 1 S22 ℓ (output) stability circle indicates the values of all ℓ that provide |in | 1. out S22 S12S21s 1 S11s S (input) stability circle indicates the values of all S that provide |out | 1. 1 (on ℓ-plane) (on s-plane) The stability criteria of an amplifier can be more conveniently expressed in terms of the stability factor K and the delta factor which have the following expressions: 1 S11 S22 K 2 S12 S21 2 2 = S11S22 - S12S21 58 2 The stability criteria in general are stated as: (i) Unconditionally Stable: K 1 and 1 ||CS| - rS | > 1 for |S22| < 1 ||Cl| - rl | > 1 for |S11| < 1 (ii) Potentially Unstable: K > 1 and || > 1 K < 1 and || < 1 or (iii) For the unilateral Case: K>1 = S11 S22 – S12 S21 =S11 S22 ||= |S11| |S22| <1 It is always stable! 59 Example: A certain GaAs MESFET has the following S parameters measured at 9GHz with a 50 Ω reference. S11 0.64 170 S12 0.0515 S21 2.1030 S22 0.57 95 Compute: a. the delta factor,Δ b. the stability factor, K c. plot the input and output stability circles. Solution: a. The delta factor, = S11S22 - S12S21 0.64 170 o x 0.57 95 o 0.0515 o x 2.1030 o 0.30110 o 0.30 1 2 0.09 b. The stability factor K, 2 K 2 1 S11 S22 2 S12 S21 2 K 2 2 1 0.64 0.57 0.30 2 2 0.05 x 2.10 1.71 1 60 c. Input and output stability circles, Center of input stability circle : cs S 11 S 22 2 S11 * * 2 * 0.64 170 o 0.30111.45 x 0.5795 o 1.50176.42 o 2 2 0.64 0.30 Radius of input stability circle : rs S12S 21 2 S11 2 0.05 x 2.10 2 0.64 0.30 0.33 2 Center of output stability circle : c * S 22 S11* 2 2 S 22 * 0.57 95 o 0.30111.45 x 0.64170 o 1.70103.32 o 0.57 2 0.30 2 Radius of output stability circle : r S12S 21 2 S 22 61 2 0.05 x 2.10 2 0.57 0.30 2 0.48 8. Constant Gain Circles i. Unilateral Case, S12 =0 Gt 1 s 2 1 S11 s 2 S21 1 2 2 1 S22 2 For any arbitrary value of s and ℓ, the transducer power gain may vary between its maximum and minimum values. Gain equation can be used to plot input (Gs) and output (Gℓ) gain circles for various s and ℓ values. Gt can be re-written as: G t Gs Gd G where Gs 1 s 2 1 S11 s 2 , G d S21 , G 2 1 2 1 S22 2 The maximum value of Gs is obtained when s = S11*. G s max 1 1 S11 Define 2 gs Gs G s max Mapping constant gs values into the Γs plane form constant input gain circles where the radius and the center of the circles are given by: Rs 1 g s 1 S11 1 S11 2 2 1 gs * g s S11 Cs 1 S11 1 g s 62 ii. Bilateral case , S12 0 It is tedious to plot constant gain circles for bilateral case where in is a function of ℓ, and out is a function of s. In practice, constant operating power gain circles (for any arbitrary chosen ℓ, conjugately match in to s) or constant available power gain circles (for any arbitrary chosen s, conjugately match out to ℓ) are plotted, as shown below. a. Constant Operating Gain Circles Transducer power gain: Gt 1 in s S When s in* 11 1 S22 G p S21 2 1 s 2 S21 1 2 2 1 S22 2 * , it is called the operation gain. 1 2 S 1 11 1 S22 2 2 S21 g p 2 1 S 22 2 Mapping gp into the ℓ-plane gives constant gain circles with centers given by: C p U p j Vp where U p g p Re C* 2 1 g p S 22 2 , Vp * C S22 S11 63 g p Im C* 2 1 g p S 22 2 and radii given by: 1 2K S 0.5 2 2 12S 21 g p S12S 21 g p rp 2 1 g p S 22 2 b. Constant Available Gain Circles Transducer power gain: Gt * out When Ga 1 s 2 1 S11 s 2 1 out 2 * S s 22 1 S11s , it is called the available gain. 1 s S s 1 22 1 S11s S21 2 1 2 2 2 1 S 11 s 2 S 21 g a S 21 2 2 Mapping ga into the Γs-plane gives constant gain circles with centers given by: Cas U as j Vas where U as g a Re C*s 2 1 g a S11 2 , Vas g a Im C*s 2 1 g a S11 2 , Cs S11 S*22 and radii given by: ras 1 2K S 2 2 12S 21 g a S12S 21 g a 2 1 g a S11 64 2 0.5 9. Maximum Available Gain Transducer power gain: 2 S21 1 Gt 2 1 2 s 1 S11 s 1 S22 S21s S12 2 For an unconditionally stable device, the maximum transducer power gain can be obtained and is known as the maximum available power gain (MAG) K S21 G MAG S12 K2 1 where K is the stability factor. in = s* = sm* MAG is obtained when and out = ℓ* = ℓm* where sm B1 B12 4 C1 2 m 2 C1 B1 1 S11 S22 2 2 2 2 2 2 B2 1 S11 S22 B2 B22 4 C 2 2 C2 C1 S11 S22* C 2 S22 S11* For positive B1 value, take - from . For negative B1 value, take + from . For positive B2 value, take - from . For negative B2 value, take + from . 65 2 Example: A certain GaAs MESFET has the following S-parameters measured at 8GHz with a 50 Ω reference. S11 0.26 55 S12 0.0880 S21 2.1465 S22 0.82 30 Find its maximum transducer power gain for the unconditionally stable case. Solution: i. Compute the delta factor and the stability factor K. 0.26 55x 0.82 30 0.0880x 2.1465 0.3488 62.9 0.3488 1 2 0.1217 2 K 2 1 0.3488 0.26 0.82 2 0.08x 2.14 2 1.1148 1 ii. Calculate the maximum available gain. 2.14 1.1148 1.1148 2 1 0.08 16.645 G MAG 12.2dB iii. Γsm and Γℓm can also be determined. sm 0.487147.6 m 0.89332.6 66 10. Steps for Narrowband Design Four categories of narrowband reflective match amplifier design: i. Maximum gain design ii. Optimum noise figure design iii. Design for maximum gain with a specific noise performance iv. Design for minimum input reflection coefficient and maximum gain with a specific noise performance Reflective match amplifier design steps: Step1: Step 2: Step 3: Step 4: Step 5: Step 6: List specifications of the amplifier to be designed. Choose a device and amplifier topology that will meet the specifications. Measure the S-parameters of the device against the specifications at the respective bias point. Check the stability conditions. Compute s and ℓ. Design the input and output matching networks. Unconditionally Stable 1. Compute Γsm and ℓm. 2. Calculate MAG. Conditionally Stable 1. Plot stability circles and operating/available circles on a Smith Chart. 2. Determine ℓ and Γs that will result ℓ and Γs in the stable region and the combination of ℓ and Γs will result in the optimum power gain. 67 V. Microwave Amplifier Implementation Single stub microstrip line matching - for narrowband design. There are two types of microstrip line matching stubs: open stub short stub For microstrip line stub-matching, we consider only parallel stubs. The load impedance is normalized and converted into admittance for the purpose of parallel stub-matching. The Smith Chart is thus used as an admittance chart. On the admittance Smith Chart, the open-end admittance is located at the left-most point of the greatest circle and the short-end admittance is located at the right-most point of the greatest circle. The length of a stub is measured in the clockwise direction. The conversion formulas between reflection coefficients and NORMALIZED impedance are: z 1 1 and z 1 z 1 where z can be zs, zℓ, zin, zout, and Γ can Γs, Γℓ, Γin, Γout. In general, it is easier to locate a normalized impedance/admittance into the Smith Chart than a reflection coefficient. The matching procedure will be illustrated by the following examples. 68 Example 1: A GaAs MESFET amplifier has the following source and load reflection coefficients measured at 9GHz with a 50ohm system:s = 0.606 155o ℓ = 0.707 120o. Design the input and output matching networks by using opencircuited and short-circuited shunt stubs. Solution: For input matching network: 1. Convert the reflection coefficient s into the normalized source impedance zs and locate it as point A on the Smith Chart. Locate also the normalized source admittance ys which is diagonally opposite point A and is denoted as point B on the Smith Chart. zs = 0.26+j 0.21 ys = 2.33-j 1.88 2. Draw an arc with O-B as the radius and read the value at point C, which is the meeting point of the arc with the unit resistance circle. yc = 1+j 1.70 3. From point O at the origin to point C, a shunt opencircuited stub with a length 0.166λ is needed. lshunt = 0.166λ 69 4. From point C to point B a series line of 50 Ω with a length of 0.105λ is needed for transforming the admittance at point C to that at point B. lseries = 0.105λ For output matching network: 5. Convert the reflection coefficient ℓ into the normalized load impedance zℓ and locate it as point A on the Smith Chart. Locate also the normalized load admittance yℓ which is diagonally opposite point A and is denoted as point B on the Smith Chart. zℓ = 0.22+j 0.56 yℓ = 0.65-j 1.55 6. Draw an arc with O-B as the radius and read the value at point C, which is the meeting point of the arc with the unit resistance circle. yc = 1 -j 2.0 7. From point O at the origin to point C a shunt short-circuited stub with a length 0.074λ is needed. lshunt = 0.074λ 8. From point C to point B a series line of 50 Ω with a length of 0.02λ is needed for transforming the admittance at point C to that at point B. lseries = 0.02λ The completed matching equivalent networks are shown: 70 Example 1a Example 1b 71 Example 2: A GaAs MESFET amplifier has the following parameters measured at 6GHz with a 50 Ω reference. Source reflection coefficient for maximum power gain: sm = 0.761 177o Load reflection coefficient for maximum power gain: ℓm = 0.719 104o Maximum available power gain GMAG = 12dB Design the input and output matching networks by using 50 Ω microstrip lines as shown below: 72 Solution: 1. Convert sm and ℓm into zsm and zℓm and locate them on the Smith Chart. zsm = 0.14+j 0.003 zℓm = 0.26+j0.75 2. Locate the normalized admittances from the Smith Chart. ysm = 7.50-j1.60 yℓm = 0.40-j1.20 3. Use the distances from the origin of the Smith Chart to ysm and yℓm as radii and draw arcs in the counter-clockwise direction (toward the load) and stop at points A and B on the unity resistance circle. Read yA = 1+j2.40 at point A yB = 1-j2.10 at point B 4. Realize two series lines. If alumina substrate is used, with εr of 10 and w/h of 0.95 (Zo = 50 Ω). The wavelength is: λ=0.39 λo=0.39x5=1.95cm at 6GHz. The length of the input and output series 50 Ω lines are: lA =0.055λ=0.055x1.95=0.11cm lB =0.046λ=0.046x1.95=0.09cm 5. Realize two shunt elements. Two shunt open stubs are needed to contribute j2.40 and –j2.10 for neutralizing the susceptance. The length of the input shunt open stub for j2.40 is: ls =0.187λ=0.187x1.95=0.36cm The length of the output shunt open stub for -j2.10 is: lo =0.321λ=0.321x1.95=0.63cm 73 The completed matching equivalent networks are shown: Example 2 74 Example 3: A GaAs MESFET has the following S-parameters measured with Vds= 4V, Ids =30mA, at 1 GHz with a 50 Ω system. S11 = 0.614 –160o S21 = 4.8 80o (i) (ii) (iii) S12 = 0 S22 = 0.682 –97o Design a narrowband amplifier for maximum power gain. Use a transmission line section and an opencircuited shunt stub for the input matching network, a transmission line section and a short-circuited shunt stub for the output matching network, respectively. The characteristic impedance for all these lines are taken to be 50 Ω. (l1 = 0.159 , l2 = 0.099 , l1’= 0.077 , l2’ = 0.051 ) Defined the maximum unilateral transducer power gain Gtmax of a transistor, and hence find the G tmax of above amplifier designed. (18.4dB) If the amplifier is built on an Al2O3 substrate with r = 10 and h=0.625mm. Find the lengths and widths of all the lines in the matching circuit. (g= 11.4cm, w=0.625mm) 75 Solution: Maximum power gain is obtained when s = S11* and ℓ = S22*. (i) For the input matching network: 1. Convert the source reflection coefficient s =0.614160° into a normalized impedance and enter as point A on the Smith Chart. Read the normalized admittance at point B: ys =2.8-j 1.8 2. Draw an arc with OB as the radius and read the value at point C. yc =1 +j 1.55 3. From point O at the origin to point C a shunt opencircuited stub with a length l 1 =0.159λ is needed. 4. From point C to point B, a series line of 50 Ω with the length of l2=0.099λ is needed. (ii) For the output matching network: 5. Convert the load reflection coefficient ℓ = 0.68297° into a normalized impedance and enter as point D on the Smith Chart. Read the normalized admittance at point E: yℓ =0.45-j1.09 6. Draw an arc with OE as the radius and read the value at point F. yF =1 - j1.9 7. From point O at the origin to point F a shunt shortcircuited stub with a length l1’ = 0.077λ is needed. 8. From point E to point F a series line of 50ohm with the length of l2’ = 0.051λ is needed. 76 (iii) The unilateral transducer power gain of the device is defined as the forward power gain having its S12 0 or Gt 1 s 2 1 S11 s 2 1 2 S21 2 1 S22 2 and the maximum unilateral transducer power gain is obtained when s = S11* and l = S22*, G t max S21 2 1 S 1 S 2 2 11 22 1 1 (4.8) 2 2 1 (0.614) 1 (0.682) 2 69.125 18.4dB (iv) Since all line impedances are 50 Ω and r = 10, w/h=1, w1= w2= w1’= w2’= 0.625mm For 50 Ω lines, eff = 6.748, and at 1GHz, g o 11.4cm eff 1 0.159x11.4cm 18.13mm 2 0.099x11.4cm 11.29mm '1 0.077x11.4cm 8.78mm '2 0.051x11.4cm 5.81mm 77 Example 3 (VIIII) ADS design example #7 Evaluate an amplifier circuit which is designed for maximum transducer gain (unilateral case) at 1 GHz, as on page 70. Now, add on two more sets of S parameters at 0.8 GHz and 1.2 GHz. The S-parameters in 50 ohms system are: 0.8 GHz S11 S12 S21 S22 1 GHz S11 S12 S21 S22 0.61 -158deg. 0 0deg. 4.9 81deg. 0.671 -95deg. 0.614 -160deg. 0 0deg. 4.8 80deg. 0.682 -97deg. 78 1.2 GHz S11 S12 S21 S22 0.62 -162deg. 0 0deg. 4.8 79deg. 0.685 -100deg The maximum unilateral transducer power gain at 1 GHz is calculated as on page 72. The amplifier circuit topology is shown on page 70 as: Input circuit: (all lines 50 ohms) 98 Source (50 ohms) -> open-circuited shunt stub (0.159 wavelength at 1 GHz) -> transmission line (0.099 wavelength at 1 GHz) -> MESFET input Output circuit: (all lines 50 ohms) Load (50 ohms) -> short-circuited shunt stub (0.077 wavelength at 1 GHz) -> transmission line (0.051 wavelength at 1 GHz) -> MESFET output The calculation of the gain (unilateral transducer power gain) of the amplifier at 0.8 GHz and 1.2 GHz is left to students. To evaluate the unilateral transducer power gain of the amplifier at 0.8 GHz, 1 GHz and 1.2 GHz by ADS. Hint: You may use the same approach as ADS design example #5 to simulate and display. Additional works are on the defining the substrate, editing of 3 sets of Sparameters instead of 1, and connecting the lines and stubs externally to the linear two port device model before connect it to the ports. Q10. Calculate the power gain of the amplifier (device plus microstrip line matching circuits) at 0.8 GHz, 1 GHz and 1.2 GHz. Compare the results with the one shown on the display by simulation. 79