Specifications of Microwave Amplifiers: Lecture 4: Microwave Amplifiers (1) Gain (dB): power gain Component focus: bipolar junction transistors (BJT) and fieldeffect transistors (FET). Mismatch (or return loss, or VSWR) The design techniques: employ the full range of concepts of microwave transmission lines, two-port networks and Smith chart presentation. Heavily used S-parameters: The development of S-parameter matrix concepts grew from the need to characterize active devices and amplifiers in a form that recognized the need for matched termination rather than short- or open-circuit termination. Stability: The amplifiers must not oscillate at any frequencies, for the range of source and load impedances expected. Noise figure: how much noise the amplifier adds compared to background noise. 1 dB compression: the input power level where the output power deviates from linear by 1 dB. Affected by bias point and supply rails. Tied to dynamic range and power consumption. 2-tone 3rd order intercept point (IP3): When two tones (two close frequencies ω1 and ω2) are present with equal amplitudes at the input, the output exhibits an intermodulation product. IP3 is where the extrapolated 3rd order intermodulation product intersects the extrapolated linear output. Dynamic range: The difference between the maximum allowable and minimum detectable input signals. Microwave amplifiers for our consideration in this lecture: Small signal so that superposition applies, Power consumption: DC power consumption ELEC518, Kevin Chen, HKUST 1 ELEC518, Kevin Chen, HKUST 2 Modeling of Microwave Transistors and Packages Third order intermodulation output power IP3 The S parameters of a given microwave transistor can be derived from transistor equivalent circuit models based on device physics, or they can be measured directly. Generally, a manufacturer of a device intended for microwave applications will provide extensive S-parameter data to permit accurate design of microwave amplifiers. This can be verified by measurement, a step that has proven important on many occasions. For a bipolar junction transistor, in addition to intrinsic device parameters such as base resistance and collector-base capacitance, amplifier performance is strongly affected by the so-called parasitic elements associated with the device package, including base-lead and emitter-lead inductance internal to the package. Similar considerations apply to microwave field-effect transistors. The magnitude and phase angle of each of the S parameters typically vary with frequency, and characterization over the complete range of interest is necessary. Dynamic range of a realistic amplifier ELEC518, Kevin Chen, HKUST 3 The S parameters also typically vary with bias. For large-signal applications, bias-dependent S parameters need to be characterized and modeled. ELEC518, Kevin Chen, HKUST 4 ELEC518, Kevin Chen, HKUST 5 Features of interests for RF active devices: ELEC518, Kevin Chen, HKUST 6 How do RFICs/MMICs look like? (1) Maximum power gain bandwidth (2) Minimum noise figure (3) Maximum power-added efficiency (4) Low thermal resistance (5) High temperature of operation and reliability (6) Low on-resistance/high off-resistance (7) High linearity (8) Low power dissipation (9) Low leakage current under cut-off operation (10) Low 1/f noise (11) Multifunctionality (12) Low single power supply (13) Semi-insulating substrate (14) Mature technology (15) Low cost ELEC518, Kevin Chen, HKUST 7 ELEC518, Kevin Chen, HKUST 8 GaAs MESFET • Gate barrier is formed by the Schottcky contact between the gate metal and doped GaAs • Higher operating frequency are achieved as a result of the higher electron mobility of GaAs compared to that of Silicon. An example of component values for a GaAs MESFET S-parameter characteristics of a GaAs MESFET 2 Cross section of a typical GaAs MESFET S 21 > 1 Intrinsic small-signal equivalent circuit S12 : Packaged MESFET model needs to include parasitics, such as series resistance and inductance at each terminal. ELEC518, Kevin Chen, HKUST 9 Unilateral current-gain cutoff frequency, fT Short-circuit (at output) current gain under the unilateral condition is defined as Gisc = Id g V g = m c = m Ig Ig ωC gs fT is defined as the upper frequency limit when the short-circuit gm current gain is unity. fT = S12 is solely determined by Cgd, which is usually very small. In this case, the device is said to be unilateral, and S 12 =0 ELEC518, Kevin Chen, HKUST 10 • The choice of DC biasing points depends on the application (lownoise, high-gain, high-power), the class of the amplifier (class A, class B, class AB). • DC bias voltage must be applied to the gate and drain, without disturbing the RF signal paths. • The input and output decoupling capacitors are needed to block DC from the input and output lines. 2πC gs DC characteristics Representing the gain Biasing and decoupling circuit ELEC518, Kevin Chen, HKUST 11 ELEC518, Kevin Chen, HKUST 12 Figure of merit: Physical layout of a MESFET. The maximum available gain (MAG) 2 f 1 MAG = T f 4 R / R + 4 π f C ds T gd ( R + Rg + πf T LS ) Where, R = Rg + Ri + RS + πfT LS fT = gm 2πC gs ELEC518, Kevin Chen, HKUST 13 ELEC518, Kevin Chen, HKUST This shows that MAG rolls of by 6 dB/octave. The frequency at which MAG is unity signifies the maximum frequency of operation and is given by, f max = f T [4 R / Rds + 4πf T C gd ( R + Rg + πf T LS )] −1 / 2 ELEC518, Kevin Chen, HKUST 15 14 Si bipolar transistor (BJT) Current driven I e = I S [exp( qVbe / kT ) − 1] ELEC518, Kevin Chen, HKUST 16 Small-signal equivalent circuit for a microwave bipolar transistor q I ( mA) ∂I gm = c = α0 I e = e 26 ∂Vbe kT fT 2 f max = 8πrbCC fT = 1 2πτ ec τec: the transit time, or the delay time from the emitter to collector Typical component values fT is given by fT = Preferred over GaAs FETs at frequencies below 2 to 4GHz (may not be true anymore) ELEC518, Kevin Chen, HKUST 17 gm 2πCπ ELEC518, Kevin Chen, HKUST Heterostructure Field-Effect Transistors (HFETs) Heterojunction bipolar transistors (HBT) High electron mobility transistor (HEMT) or Modulated doped FET (MODFET): for high carrier mobilities and speed Key advantage: Higher emitter injection efficiency The doping profile of HBT ELEC518, Kevin Chen, HKUST 19 18 Energy band diagram of HBT ELEC518, Kevin Chen, HKUST 20 Two-port network for amplifier analysis SiGe HBT Objective: try to derive parameter expressions in terms of the S-parameter of the network. Pick your position! But be flexible. Power Gain G, Available Gain GA, Transducer Gain GT: PL power delivered to the load = G= Pin power input to the network Pavout power available from the network = GA = power available from the source Pavs PL power delivered to the load = GT = Pavs power available from the source ELEC518, Kevin Chen, HKUST 21 When the input and output are both conjugately matched to the twoport, all the gains are maximized and G = GA = GT . Definitions of Γ L, Γ s, Γ in and Γ out: ZL - Zo ΓL = ZL + Zo , the reflection coefficient of the load Zs - Zo Γs = Zs + Zo , the reflection coefficient of the source Zin - Zo S12S21ΓL Γin = = S11+ , the input reflection coefficient Zin + Zo 1-S22ΓL Zout - Zo S12S21Γs Γout = = S + , the output reflection coefficient 22 Zout + Zo 1-S11Γs A typical S-parameter table for a GaAs FET f GHz 3.0 4.0 5.0 S11 S21 S12 S22 0.80/-89° 0.72/-116° 0.66/-142° 2.86/99° 2.60/76° 2.39/54° 0.03/-56° 0.03/-57° 0.03/-62° 0.76/-41° 0.73/-54° 0.72/-68° ELEC518, Kevin Chen, HKUST ELEC518, Kevin Chen, HKUST 22 Power Gain Equations The equations for the various power gain definitions are 1) PL G=P = 2) GA = 3) GT = in 1 - lΓLl 2 1 lS21l2 2 1 - lΓinl l1 - S22ΓLl 2 Pavout 1 - lΓsl 2 1 = lS l2 Pavs l1 - S11Γsl 2 21 1 - lΓoutl2 PL 1 - lΓsl2 1 - lΓLl 2 2 = lS l 21 Pavs l1 - ΓinΓsl2 l1 - S22ΓLl 2 2 1 - lΓsl 1 - l ΓLl2 2 = lS l 21 l1 - S11Γsl2 l1 - ΓoutΓLl2 Read page 606-609 of Pozar for the derivation. 23 ELEC518, Kevin Chen, HKUST 24 For a unilateral network, S12=0 and Γin = S11 if S12=0 (unilateral network) 1) 2) Model of a single-stage microwave transistor amplifier Zo Γout = S22 if S12=0 (unilateral network) Input Matching Circuit Gs We can then define the unilateral transducer power gain, GTU, which is given by 2 2 2 S 21 1 − ΓS 1 − ΓL GTU = 2 2 1 − S11ΓS 1 − S 22 ΓL )( ( ) Output Matching Circuit GL Transistor [S] Go Γs Γ in Γout Γ Zo L The transducer gain GT can be expressed as the product of three gain contributions GT=GsGoGL, where Go = lS21l 2 , ELEC518, Kevin Chen, HKUST GTU = G sU = ( S 21 1 − ΓS 2 26 GTU (dB) = Gs (dB) + Go (dB) + GL (dB). )(1 − Γ ) 2 We can maximize Gs and GL by setting Γs = S11* and ΓL = S22* so that Gsmax = 1 and 1 - lS11l2 GLmax = 1 , so that 1 - lS22l2 L 1 − S11ΓS 1 − S 22 ΓL 2 1 - lΓ s l2 , where the subscript U indicates unilateral gain. l1 - S 11 Γ s l2 In practice, the difference betw een G T and G TU is often quite sm all, as it is desirable for devices to be unilateral if possible. ELEC518, Kevin Chen, HKUST ELEC518, Kevin Chen, HKUST The components of GTU can also be expressed in decibel form, so that If the device is unilateral, or sufficiently unilateral so that S 12 is sm all enough to be ignored, the unilateral transducer gain G TU is sim plified because 2 1 - lΓsl 2 1 - l ΓLl2 and G = L l1 - ΓinΓsl2 l1 - S22ΓLl2 25 For a unilateral network, S12=0 and Γin = S11 if S12=0 (unilateral network) 1) Γout = S22 if S12=0 (unilateral network) 2) 2 Gs = 27 GTUmax = 1 1 lS l2 1 - lS11l2 21 1 - lS22l2 Note that, if lS11l=1 or lS22l=1, GTUmax is infinite. This raises the question of stability, which will be examined next. ELEC518, Kevin Chen, HKUST 28 These are defined by circles, called stability circles, that delimit lΓinl = 1 and lΓoutl = 1 on the Smith chart. Stability In a two-port network, oscillations are possible if the magnitude of either the input or output reflection coefficient is greater than unity, which is equivalent to presenting a negative resistance at the port. This instability is characterized by The radius and center of the output and input stability circles are derived from the S parameters on (see pg. 613-614 of Pozar). Output stability circle lΓinl > 1 or lΓoutl > 1, which for a unilateral device implies lS11l > 1 or lS22l > 1. Thus the requirements for stability are S12S21ΓL lΓinl = lS11+ < 1 and 1-S22ΓL l S12S21Γs lΓoutl = lS22+ 1-S11Γs l < 1 ELEC518, Kevin Chen, HKUST Input stability circle Where, ∆ = S11S22 − S12 S21 29 ELEC518, Kevin Chen, HKUST Stable and unstable regions in the ΓL plane Stable and unstable regions in the ΓS plane load stability circle Source stability circle ELEC518, Kevin Chen, HKUST 31 ELEC518, Kevin Chen, HKUST 30 32 Practical microwave transistors: unconditionally stable or potentially unstable with K < 1 and ∆ < 1 . Stability Consideration: Unconditional stable condition: 2 2 In potentially unstable transistors, most of the practical values of K are such that 0 < K < 1 --- source and load stability circles intersect the boundary of the Smith chart. 2 1 − S11 − S 22 + ∆ K= > 1 and 2 S12 S 21 If -1 < K < 0, most region of the Smith chart is unstable. Some transistor configurations (e.g. some CB configurations) used in oscillator designs are potentially unstable with negative values of K. l∆l < 1, where ∆, the determinant of the scattering matrix, is ∆ = S11S22 - S12S21 Conditionally stable: K < 1, operating points for ΓS and ΓL must be chosen in the stable region, and it is good practice to check the stability at several frequencies near the design frequency. ELEC518, Kevin Chen, HKUST In the potentially unstable situations, the real part of the input and output impedances can be negative for some source and load reflection coefficients. 33 Example: ELEC518, Kevin Chen, HKUST 34 Solutions: conditionally stable at 500 MHz and 1GHz, unconditionally stable at 2 GHz and 4 GHz. Input stability circles ELEC518, Kevin Chen, HKUST 35 output stability circles ELEC518, Kevin Chen, HKUST 36 Resistive loading and negative feedback: improve stability Even when the selection of ΓL and ΓS produces unstable operation, the circuit can be made stable if the total input and output loop resistance is positive Example: using a resistive loading to stabilize a potentially unstable transistor Re( Z s + Z in ) > 0 and Re( Z L + Z out ) > 0 Adding a resistive load or adding negative feedback. Not recommended in narrowband amplifiers because of the resulting degradation in power gain, noise figure, and VSWRs. Narrowband amplifier design with potentially unstable transistors is best done by the proper selection of ΓL and ΓS to ensure stability. ELEC518, Kevin Chen, HKUST 37 All four choices of resistive loading affect the gain performance of the amplifier. In practice, resistive loading at the input is not used because it produces a significant deterioration in the noise performance of the amplifier. Shunt resistor loading at the output produces the most acceptable trade-off between gain and stability and is most used in practice. ELEC518, Kevin Chen, HKUST 39 ELEC518, Kevin Chen, HKUST 38