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An Introduction To Two – Port Networks

An Introduction To Two – Port Networks. Dept. of Electronics & Telecommunication Engineering. 1. VM Umale. Two Port Networks. Generalities:. The standard configuration of a two port:. I 1. I 2. The Network. +. +. Input Port. Output Port. V 1. V 2. _. _. The network ?.

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An Introduction To Two – Port Networks

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  1. An Introduction To Two – Port Networks Dept. of Electronics & Telecommunication Engineering 1 VM Umale

  2. Two Port Networks Generalities: The standard configuration of a two port: I1 I2 The Network + + Input Port Output Port V1 V2 _ _ The network ? The voltage and current convention ? * notes Dept. of Electronics & Telecommunication Engineering 2 VM Umale

  3. Two Port Networks Network Equations: V1 = z11I1 + z12I2 V2 = z21I1 + z22I2 V2 = b11V1 - b12I1 I2 = b21V1 – b22I1 Impedance Z parameters V1 = h11I1 + h12V2 I2 = h21I1 + h22V2 I1 = y11V1 + y12V2 I2 = y21V1 + y22V2 Admittance Y parameters Hybrid H parameters Transmission A, B, C, D parameters V1 = AV2 - BI2 I1 = CV2 - DI2 I1 = g11V1 + g12I2 V2 = g21V1 + g22I2 Dept. of Electronics & Telecommunication Engineering 3 VM Umale

  4. Of these four variables V­1, V2, i1 and i2, two can be selected as independent variables and the remaining two can be expressed in terms of these independent variables. This leads to various two part parameters out of which the following three are more important. Dept. of Electronics & Telecommunication Engineering 4 VM Umale

  5. Hybrid Parameters or h-parameters • If the input current i1 and output Voltage V2 are takes as independent variables, • Then input voltage V1 and output current i2 can be written as: • V1 = h11 i1 + h12 V2 • i2 = h21 i1 + h22 V2 • The four hybrid parameters : h11, h12, h21 and h22 are defined as follows. • h11 = [V1 / i1] with V2 = 0, :I/P Resistance with output port short circuited. • h12 = [V1 / V2] with i1 = 0, : reverse voltage transfer ratio with i/p port open circuited. • h21 = [i2 / i1] with V2 = 0, : Forward current gain with output part short circuited. • h22 = [i2 / V2] with i1 = 0, : Output admittance with input part open circuited. Dept. of Electronics & Telecommunication Engineering 5 VM Umale

  6. The dimensions of h – parameters are as follows: h11 - Ω h12 – dimension less. h21 – dimension less. h22 – mhos as the dimensions are not alike, (i.e) they are hybrid in nature, and these parameters are called as hybrid parameters. Dept. of Electronics & Telecommunication Engineering 6 VM Umale

  7. Two Port Networks Hybrid Parameters: The equations for the hybrid parameters are: V2 = 0 I1 = 0 V2 = 0 I1 = 0 * notes Dept. of Electronics & Telecommunication Engineering 17 VM Umale

  8. Two Port Network Dept. of Electronics & Telecommunication Engineering 8 VM Umale

  9. Hybrid Parameters: V1 = h11 i1 + h12 V2 I2 = h21 i1 + h22 V2 ↓ ↓ V1 = hi i1 + hr V2 I2 = hf i1 + h0 V2 The equations for the hybrid parameters are: V2 = 0 I1 = 0 V2 = 0 I1 = 0 Dept. of Electronics & Telecommunication Engineering 9 VM Umale

  10. Two Port Networks Hybrid Parameters: The following is a popular model used to represent a particular variety of transistors. hi hrV2 ho hf I1 We can write the following equations: Dept. of Electronics & Telecommunication Engineering 11 VM Umale * notes

  11. Hybrid h-Parameter model for an amplifier • The equivalent circuit of a transistor can be drawn using simple approximation by retaining its essential features. • These equivalent circuits will aid in analyzing transistor circuits easily and rapidly. •  A transistor can be treated as a two part network. The terminal behavior of any two part network can be specified by the terminal voltages V1 & V2 at parts 1 & 2 respectively and current i1 and i2, entering parts 1 & 2, respectively, as shown in figure. Dept. of Electronics & Telecommunication Engineering 12 VM Umale

  12. Transistor Hybrid Model • Use of h – parameters to describe a transistor have the following advantages: • h – parameters are real numbers up to radio frequencies . • They are easy to measure • They can be determined from the transistor static characteristics curves. • They are convenient to use in circuit analysis and design. • Easily convert able from one configuration to other. • Readily supplied by manufactories. Dept. of Electronics & Telecommunication Engineering 13 VM Umale

  13. Transistor Hybrid Model CE Configuration In common emitter transistor configuration, the input signal is applied between the base and emitter terminals of the transistor and output appears between the collector and emitter terminals. The input voltage (Vbe) and the output current (ic) are given by the following equations: Vbe = hie.ib + hre.Vc ie = hfe.ib + hoe.Vc Transistor Hybrid Model CE Configuration Dept. of Electronics & Telecommunication Engineering 14 VM Umale

  14. Transistor Hybrid Model CB Configuration Dept. of Electronics & Telecommunication Engineering 15 VM Umale

  15. Transistor Hybrid Model CB Configuration Where hie =(∂f1/∂iB)Vc = (∂vB/∂iB)Vc = (ΔvB /ΔiB)Vc = (vb / ib)Vc hre =(∂f1/∂vc)IB = (∂vB/∂vc) IB = (ΔvB /Δvc) IB = (vb /vc) IB hfe =(∂f2/∂iB)Vc = (∂ic /∂iB)Vc = (Δ ic /ΔiB)Vc = (ic / ib)Vc hoe= (∂f2/∂vc)IB = (∂ic /∂vc) IB = (Δ ic /Δvc) IB = (ic /vc) IB The same theory is extended to other configurations including CB and CC Dept. of Electronics & Telecommunication Engineering 16 VM Umale

  16. Transistor Hybrid Model CC Configuration Dept. of Electronics & Telecommunication Engineering 15 VM Umale

  17. Hybrid Model and Equations for the transistor in three different configurations are are given below. Dept. of Electronics & Telecommunication Engineering 17 VM Umale

  18. Analysis of Transistor Amplifier using Complete h-Parameter Model In the h-parameter model consider the load Resistance RL and input signal Vs. The expressions for Current gain, Voltage gain ,input and output impedance are: 1. Current Gain: Ai=-hf/(1+hoRL) Where Ai is the current amplification or current gain The overall current gain taking source resistance is given by: Ais=Ai * (Rs/Zi + Rs) where Zi input impedance Rs source resistance Dept. of Electronics & Telecommunication Engineering 18 VM Umale

  19. Analysis of Transistor Amplifier using Complete h-Parameter Model 2)Input Impedance(Zi) Zi= hi+hrAiRL 3) Voltage Gain(Av): Av=(Ai * RL)/ Zi Voltage gain taking source resistance is given by Avs=(Av * Zi)/(Zi+Rs) 4) Output Admittance(Yo) Yo=ho-hf * hr/(hi+Rs) Dept. of Electronics & Telecommunication Engineering 19 VM Umale

  20. Analysis of Transistor Amplifier using simplified h-Parameter Model Common Emitter Configuration Fixed Bias configuration: Input Impedance Zi = RB || hie Output Impedance Zo=RC || (1/hoe) Voltage gain Av=-hfe * (RC || (1/hoe) /hie Current Gain Ai=hfe * RB/(RB + hie) Voltage Divider Configuration: Input impedance Zi=(RB1 || RB2)|| hie Output Impedance Zo=RC ||(1/hoe) Voltage gain Av=-hfe * [RC || (1/hoe)]/hie Current gain Ai=hfe * (RB1||RB2)/(RB1|| RB2) + hie Dept. of Electronics & Telecommunication Engineering 20 VM Umale

  21. Basic Laws of Circuits End of Lesson Two-Port Networks

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