10. Noise and active RF components

10.1 Noise in microwave circuit 전자 Lattice scattering 원자핵

Noise power, noise voltage Measurement setup: Spectrum analyzer Noise power : Planck 법칙에 의한 radiation Planck 법칙에 의한 복사 전력 k: Boltzmann constant (1.38e-23 J/K) B : bandwidth in Hz T : Absolute temperature in Kelvin R : resistance in Ω. Noise voltage :

Equivalent noise temperature: Te Equivalent noise power Figure 10-4 (p. 490) The equivalent noise temperature, Te, of an arbitrary white noise source.

Equivalent noise temperature of an amplifier Figure 10-5 (p. 491) Defining the equivalent noise temperature of a noisy amplifier. (a) Noisy amplifier. (b) Noiseless amplifier.

Noise temperature Figure 10-6 (p. 492) The Y-factor method for measuring the equivalent noise temperature of an amplifier.

Dynamic range of an amplifier Power output threshold 입력신호와 상관없이 회로 자체에서 생기는 noise로 인한 출력

Noise figure Noise figure : 회로 자체에서 생기는 noise로 인해 SNR이 얼마나 나빠졌는가의 척도

Noise figure of a lossy network Lossy network의 noise figure는 loss와 같다. Noise는 loss에 의해 감쇄되지 않고 온도와 관련됨.

Noise figure of a cascaded system

Example 10.2 Noise analysis of a wireless receiver 아래 블록 다이어그램은 무선 단말기의 수신 부이다. Feeding antenna의 noise temperature가 150K일 때 출력 신호의 noise 전력을 구하라. 또한 출력 신호를 구분 가능한 최소의 SNR이 20dB라고 할 때 입력신호의 최소 전압도 구하라.

10.2 Dynamic range and inter-modulation distortion DC output Linear output Squared output

Gain compression a3의 부호는 a1과 반대가 되는 경우가 많아서 입력 전압이 커질수록 gain이 줄어든다.

Inter-modulation distortion

Output signal from a non-ideal amplifier 입력 신호 출력 신호 Filter로 제거 가능 Filter로 제거 가능 Filter로 제거 불가능

Third-Order intercept point 주파수 ω1 성분의 power 주파수 2ω1 - ω2 성분의 power 출력 주파수 ω1 , 2ω1 - ω2 두 성분의 power가 같아질 때 입력 전력.

Dynamic range Linear dynamic range : P1dB /N0 Spurious free dynamic range : Pω1/P2ω1-ω2 (P2ω1-ω2 = N0) Figure 10-17 (p. 506) Illustrating linear dynamic range and spurious free dynamic range.

Intercept point of a cascaded system

Example 10.5 For amplifier For mixer

10.3 RF diode characteristics Diode 의 비선형 효과를 이용하여 signal detection, demodulation, switching, frequency multiplication, oscillation 회로를 만든다. Figure 10-20 (p. 510) Basic frequency conversion operations of rectification, detection, and mixing. (a) Diode rectifier. (b) Diode detector. (c) Mixer.

Diode 종류 (2) Schottky diode (1) pn-junction diode Turn on voltage : 0.7V Turn on voltage : 0.25V high frequency에서 동작을 위해 pn-junction diode보다 Schottky barrier diode를 사용한다. pn-junction은 reverse recovery time으로 ~100ns 이상의 switching time이 필요하나 Schottky diode는 ~100ps 도 가능.

Unbiased PN junction ID : Diffusion current. IS : Drift current Electric field

Minority-carrier distribution in a forward-biased pn junction Minority-carrier distribution in a forward-biased pn junction. It is assumed that the p region is more heavily doped than the n region; NA @ ND.

(3) p-i-n diode 등가 회로 pn-junction 사이에 intrinsic (doping이 안된 상태) 반도체가 있어 역방향일 때 C (capacitance)를 더욱 줄여주고, 순방향일 때 직렬 저항을 조절 가능하게 함. RF switch

Diode package

RF diode i~v characteristics Large signal model n=1.2 for Schottky barrier diode, n=2 for point contact silicon diode Small signal model approximation DC bias current

Contact, current-spreading resistance Shunt capacitance lead inductance Contact, current-spreading resistance Shunt capacitance Figure 10-22 (p. 511) Equivalent AC circuit model for a Schottky diode. Junction capacitance, junction resistance

Diode rectifiers Bias current DC rectified current

Diode detectors m : modulation index, 0<m<1 입력 power에 비례한 출력이므로 square law detector

Diode detector output Figure 10-24 (p. 513) Square-law region for a typical diode detector.

Pin diodes and control circuits Microwave switch mechanical type: high power, slow switching speed electronic type : PIN diode, FET. High speed operation (~10ns)

Equivalent circuit : typical values Figure 10-25 (p. 515) Equivalent circuits for the ON and OFF states of a PIN diode. (a) Reverse bias (OFF) state. (b) Forward bias (ON) state.

Single-pole PIN diode switches Figure 10-26 (p. 515) Single-pole PIN diode switches. (a) Series configuration. (b) Shunt configuration.

Switch equivalent circuits Figure 10-27 (p. 516) Simplified equivalent circuits for the series and shunt single-pole PIN diode switches. (a) Series switch. (b) Shunt switch.

Microwave network analysis 1-port network 2-port network

Device characterization Impedance and Admittance Matrix - Generalize Z concept to N-port - Arbitrary N-port Network Impedance matrix t2 V1+, I1+ t3 t1 t4 V1-, I1- t1 tN VN+,IN+ VN-, IN- Admittance matrix

Measurement of impedance parameter Two port network + - 주파수가 높은 경우 open-circuit만들기 어려움. (parasitic capacitance 때문) Admittance parameter인 경우는 short circuit만들기 어려움. (parasitic inductance때문)

Scattering Matrix - in accord with direct measurement - incident, reflected & transmitted wave - easy to adeve impedance matching at high frequency All other part j≠k matched → no reflection Vk→ 0 Sii reflection coefficient Sji transmission coefficient

Measurement of S-parameters Impedance matching 된 상태 Port 1 Port 2 Transfer switch Source B R A S-Parameter Test Set DUT Fwd Rev

Example 4.4 S-parameter 계산 Port 1 2 ⅰ) Thereby S11=0 Symmetry of circuit S22=0 ⅱ) since S11=S22=0 & part 2 is terminated with 50ohm

Pin diode phase shifters A switched line phase shifter

Loaded line phase shifters Basic circuit

Practical loaded-line phase shifter

A reflection phase shifter using a quadrature hybrid

7.5 Quadrature hybrid coupler

10.4 RF transistor characteristics Table 10.2 Performance characteristics of microwave transistors Device Si BJT Si CMOS SiGe HBT GaAs MESFET GaAs HEMT GaAs HBT Frequency range (GHz) 10 20 30 40 100 60 Typical gain (dB) 10-15 10-20 5-20 Noise Figure (dB) 2.0 (2GHz) 1.0 (4GHz) 0.6 (8GHz) 1.0 (10GHz) 0.5 (12GHz) 4.0 Power capacity High Low Medium Cost Single polarity power supply Yes No

FETs 52 Figure 10-33 (p. 523) (a) Cross section of a GaAs MESFET; (b) top view, showing drain, gate, and source contacts.

Equivalent circuit for a microwave FET Common-source configuration Unity gain frequency (Short circuit current gain)

DC bias circuit Figure 10-35 (p. 524) (a) DC characteristics of a GaAs FET; (b) biasing and decoupling circuit for a GaAs FET.

BJTs Figure 10-36 (p. 525) (a) Cross section of a microwave silicon bipolar transistor; (b) top view, showing base and emitter contacts.

Equivalent circuit for a microwave BJT Common-emitter configuration Unity gain frequency

DC bias circuit Figure 10-38 (p. 526) (a) DC characteristics of a silicon bipolar transistor; (b) biasing and decoupling circuit for a bipolar transistor. Zero가 되어 high frequency에서 oscillation가능성 있음. 저항 때문에 noise figure증가함. Emitter는 GND에 연결되어 있는 형태가 많이 쓰임.

DC bias network - BJT Collector current changes due to temperature variation Ic doubles every 10℃ rise. Ic when IE=0.

Example 온도가 올라가면 Ic가 커진다. 그러나 Rc가 큰 경우 변화는 미미하다.

Example

Active bias-BJT

Bias point selection-BJT

DC bias network – GaAs MESFET

Bias point selection

Active bias-GaAs

Figure 10-39 (p. 528) Layout of a hybrid microwave integrated circuit.

Figure 10-40 (p. 528) Photograph of one of the 25,344 hybrid integrated T/R modules used in Raytheon’s Ground Based Radar system. This X-band module contains phase shifters, amplifiers, switches, couplers, a ferrite circulator, and associated control and bias circuitry. Courtesy of Raytheon Company, Lexington, MA.

Figure 10-41 (p. 530) Layout of a monolithic microwave integrated circuit.

Figure 10-42 (p. 530) Photograph of a monolithic integrated X-band power amplifier. This circuit uses eight heterojunction bipolar transistors with power dividers/combiners at the input and output to produce 5 watts. Courtesy of M. Adlerstein and R. Wohlert, Raytheon Company.