Measurement of S-Parameters. Transfer of the Reference Plane. Power Waves. Graphic Representation of Waves in Circuits

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Lecture 6 RF Amplifier Design Johan Wernehag Electrical and Information Technology Lecture 6 Amplifier Design Toughest

Graphs Stability Analysis Power Definitions Design Methods Maximum Minimum Noise Figure The Vector Network Analyser

Model: S-Parameters Definition 1-port network reflection coefficient a x = incident wave b x = reflected wave 1-port

transmission parameters X, large signal scattering parameters NOTE!

1 Lecture 6 RF Amplifier Design Johan Wernehag Electrical and Information Technology Lecture 6 Amplifier Design Toughest week in the course, hang S-Parameters in there Definitions Power Waves Applications Parameter Conversion Signal Flow Graphs Stability Analysis Power Definitions Design Methods Maximum Minimum Noise Figure The Vector Network Analyser (refresher from Introduction to ) Diagnostic test 2 S-Parameters The circuit is characterized by wave quantities Model: S-Parameters Definition 1-port network reflection coefficient a x = incident wave b x = reflected wave 1-port or in matrix format: N-port network (the course only deals with s) S-parameters (scattering parameters) T, transmission parameters X, large signal scattering parameters NOTE! The definition utilizes 50W as reference impedance Definition: b = s a + s a b = s a + s a Boundary conditions: b b = s s s s a a IMPORTANT! The definition utilizes 50W as reference impedance 3 4

Measurement of S-Parameters Transfer of the Reference Plane A simple example when you need to compensate for the effect of the test cables: S-parameters including test cables: The S-parameters may

Waves At one port: Apply normalized quantities: where a and b are referred as power waves The first equations may now be written: NOTE!

2 Measurement of S-Parameters Transfer of the Reference Plane A simple example when you need to compensate for the effect of the test cables: S-parameters including test cables: The S-parameters may easily be measured if the ports are terminated by the reference impedance Z 0 = 50W (Γ L = 0 respectively Γ S = 0) The change of the waves between the reference planes: Substitute: Result: 5 6 Power Waves At one port: Apply normalized quantities: where a and b are referred as power waves The first equations may now be written: NOTE! V and I are denoted as peak values Graphic Representation of Waves in Circuits Ordinary circuit diagrams are not effective as they only represents nodes (voltages) and branches (currents). Signal flow graphs are useful tools as waves in different directions are separated and represented by nodes. example: 1-port 1-port Signal flow graph The power in the waves are: Signal flow graph The power delivered to the two-port is then: Methods for systematic analysis by signal flow graphs are depicted in chapter

S-Parameters, Parameter Conversion Stability Analysis by S-Parameters The S-parameters may be converted into y, z or ABCD parameters and vice versa without any loss of information Definition of

3 S-Parameters, Parameter Conversion Stability Analysis by S-Parameters The S-parameters may be converted into y, z or ABCD parameters and vice versa without any loss of information Definition of unconditional stability: Conversion of S-parameters results in normalised y, z and ABCD parameters Example: 1) Convert S-parameters to z parameters 2) Denormalise: Z=z 50W Note! The definition utilizes 50W as reference impedance or 9 10 Bilateral two-port Bilateral and Unilateral Two-Port Stability Analysis, Unilateral Two-Port Unilateral two-port: S 12 = 0 (does these really exist?) The unilateral two-port (S 12 = 0) is unconditionally stable if i.e. and 11 12

Stability Analysis, Bilateral Two-Port How can we show if a bilateral two-port is unconditionally stable? But if Stability Analysis, Bilateral Two-Port (cont.) not are fulfilled, what then?

After an extensive analysis the stability criteria can be reformulated as where Find all Γ L that gives Γ in = 1 and all Γ S that gives Γ out = 1 13 14 The result is stability circles: Stability

4 Stability Analysis, Bilateral Two-Port How can we show if a bilateral two-port is unconditionally stable? But if Stability Analysis, Bilateral Two-Port (cont.) not are fulfilled, what then? There may be some Γ L that provides Γ in < 1 and Γ S that provides Γ out < 1 The two-port is then considered to be conditionally stable Where is the boundary for stability? After an extensive analysis the stability criteria can be reformulated as where Find all Γ L that gives Γ in = 1 and all Γ S that gives Γ out = The result is stability circles: Stability Analysis, Bilateral Two-Port (cont.) Solve Γ out = 1 with respect to Γ S and Γ in = 1 with respect to Γ L The stability circles denotes all Γ S that equals Γ out = 1 and all Γ L that equals Γ in = 1 the circles accordingly shows the boundary for instability... Stability Circles Γ S -plane: radius centre Γ L -plane: radius centre But which Γ S and Γ L implies stability? i.e. are the Γ that provides stability found inside or outside respectively stability circle? Test at one location! It is understood that if one point is part of the stable set, e.g. in the Γ S -plane, then this holds for all other points belonging to the same set. Tip: test at the centre of the Smith chart! Why is this smart? Perform the same test in the Γ L -plane

Stability Circles (cont.) In which area is the output stable?

Stability Circles (cont.) In which area is the input stable?

S 22 < 1 stable outside the circle S 22 > 1 stable inside the circle S 11 < 1 stable outside the circle S 11

matching network Two-port network Output matching network Z L P IN G ES P AVS P AVN P L Z L Given this:

5 Stability Circles (cont.) In which area is the output stable? Test at the centre in the Γ S -plane: Γ S = 0 Γ out = S 22 is S 22 greater or less than one? Stability Circles (cont.) In which area is the input stable? Test at the centre in the Γ L -plane: Γ L = 0 Γ in = S 11 is S 11 greater or less than one? S 22 < 1 stable outside the circle S 22 > 1 stable inside the circle S 11 < 1 stable outside the circle S 11 > 1 stable inside the circle General design case Amplifier Design Power Definitions Z S E S Z S Input matching network Two-port network Output matching network Z L P IN G ES P AVS P AVN P L Z L Given this: two-port (S-parameters) and source Γ S and load Γ L available gain The stability analysis gives allowed values of Γ S and Γ L After a proper choice of Γ S and Γ L the matching networks may be designed transducer gain operating gain 19 20

The Expressed by S-Parameters Design Cases - and Noise Figure Z S G P AVS P IN P AVN ES P L Z L Approximation suitable for hand

Maximum Specific Minimum Noise Figure There is hardly no reason to use these methods for computer analysis.

sweep amplitude sweep complete information amplitude phase Calibration Attenuation and phase shift in the test cables must be

6 The Expressed by S-Parameters Design Cases - and Noise Figure Z S G P AVS P IN P AVN ES P L Z L Approximation suitable for hand calculation Amplifier Design available gain Unilateral Two-Port Bilateral Two-Port operating gain transducer gain Maximum Specific Maximum Specific Minimum Noise Figure There is hardly no reason to use these methods for computer analysis. Compromise - Noise Figure Vector Network Analysis Characterising the Device Under Test properties Network Analyser frequency sweep amplitude sweep complete information amplitude phase Calibration Attenuation and phase shift in the test cables must be compensated Calibrated reference planes are therefore created where the device under test is connected a 1 b 2 b 1 DUT a 2 Calibrated reference plane DUT 23 24

Calibration Be careful about torn connectors!

The wear and tear when connectors are connected and disconnected may result in

TOSM always check that the connectors are clean only turn the socket or the nut

contact pin may never spin round always use a torque wrench or fingers the connector

Short s and connectors for professional use are only used for a limited period until

50W Match 50W Calibrated reference planes 25 S-Parameter Measurements on a Transistor

7 Calibration Be careful about torn connectors! Calibrated reference planes will be created where the DUT is to be connected Through The wear and tear when connectors are connected and disconnected may result in measurement errors. TOSM always check that the connectors are clean only turn the socket or the nut Through measurements at known references correction data may be determined Open the contact pin may never spin round always use a torque wrench or fingers the connector may never be fastened by other tools if you tighten up to hard the thread is harmed Short s and connectors for professional use are only used for a limited period until they will be exchanged or reconditioned. 50W Match 50W Calibrated reference planes 25 S-Parameter Measurements on a Transistor 26 Lab 2 Calibration Measurement Reference plane after calibration Test board with transistor RF RF+DC BFR520 measurement PCB Bias T RF+DC RF Bias T DC DC Calibration standards Calibration standards Through Test PCB b Match 50Ω Transistor c Short Open e 27 28

Waves on Lines. Contents. ! Transmission Lines! The Smith Chart! Vector Network Analyser (VNA) ! Measurements

Waves on Lines. Contents. ! Transmission Lines! The Smith Chart! Vector Network Analyser (VNA) ! Measurements Waves on Lines If the wavelength to be considered is significantly greater compared to the size of the circuit the voltage will be independent of the location. amplitude d! distance but this is not true