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EIE 211 Electronic Devices and Circuit Design II

EIE 211 Electronic Devices and Circuit Design II. EIE 211 : Electronic Devices and Circuit Design II Lecture 9: Two-port Networks & Feedback. EIE 211 Electronic Devices and Circuit Design II. Example : Design a 2 nd order high pass active filter based on the inductor

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EIE 211 Electronic Devices and Circuit Design II

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  1. EIE 211 Electronic Devices and Circuit Design II EIE 211 : Electronic Devices and Circuit Design II Lecture 9: Two-port Networks & Feedback King Mongkut’s University of Technology Thonburi

  2. EIE 211 Electronic Devices and Circuit Design II Example: Design a 2nd order high pass active filter based on the inductor replacement King Mongkut’s University of Technology Thonburi

  3. EIE 211 Electronic Devices and Circuit Design II Second Order Active Filters based on the Two-Integrator-Loop Topology To derive the two-integrator loop biquadratic circuit, or biquad, consider the high-pass transfer function We observe that the signal (ωo/s)Vhp can be obtained by passing Vhp through an integrator with a time constant equal to 1/ωo. Furthermore, passing the resulting signal through another identical integrator results in the signal (ωo2/s2)Vhp. The block diagram on the next page shows a two-integrator arrangement. King Mongkut’s University of Technology Thonburi

  4. EIE 211 Electronic Devices and Circuit Design II From It suggests that Vhp can be obtained by using the weighted summer in Fig b. Now we combine blocks a) and b) together to obtain: King Mongkut’s University of Technology Thonburi

  5. EIE 211 Electronic Devices and Circuit Design II If we try to look at the Fig c. more carefully, we’ll find that And the signal at the output of the first integrator is –(ωo/s)Vhp, which is a band-pass function, with the center-frequency gain of –KQ, Therefore, the signal at the output of the first integrator is labeled Vbp. In, a similar way, the signal at the output of the second integrator is (ωo2/s2)Vhp, which is a low-pass function, Thus, the output of the second integrator is labeled Vlp. Note that the dc gain of the low-pass filter is equal to K. Hence, the 2-integrator-loop biquad realizes 3 basic 2nd order filtering functions simultaneously, that’s why it’s called a universal active filter. King Mongkut’s University of Technology Thonburi

  6. EIE 211 Electronic Devices and Circuit Design II Circuit Implementation We replace each integrator with a Miller integrator circuit having CR = 1/ωo and we replace the summer block with an op amp summing circuit that is capable of assigning both positive and negative weights to its inputs. The resulting ckt, known as the Kerwin-Huelsman-Newcomb or KHN biquad.

  7. EIE 211 Electronic Devices and Circuit Design II We can express the output of the summer Vhp in terms of its inputs, Vbp = –(ωo/s)Vhp and Vlp = (ωo2/s2)Vhp, as To determine all the parameters, we need to compare it to the original eq: We can match them up, term by term, and will get: King Mongkut’s University of Technology Thonburi

  8. EIE 211 Electronic Devices and Circuit Design II The KHN biquad can be used to realize notch and all-pass functions by summing weighted versions of the three outputs, LP, BP, and HP as shown. Substitute Thp, Tbp and Tlp that we found previously, we’ll get the overall transfer function from which we can see that different transmission zeros can be obtained by the appropriate selection of the values of the summing resistors. For instance, a notch is obtained by selection RB = ∞ and King Mongkut’s University of Technology Thonburi

  9. EIE 211 Electronic Devices and Circuit Design II Two-Port Network Parameters King Mongkut’s University of Technology Thonburi

  10. EIE 211 Electronic Devices and Circuit Design II Characterization of linear, two-port networks Before we begin a discussion on the topic of oscillators, we need to study feedback. However, in order to understand how the feedback works, we also need to first learn the two-port network parameters. A two-port network has four port variables: V1, I1, V2 and I2. If the two-port network is linear, we can use two of the variables as excitation variables and the other two as response variables. For example, the network can be excited by a voltage V1 at port 1 and a voltage V2 at port 2, and the two current I1 and I2 can be measured to represent the network response. There are four parameter sets commonly used in electronics. They are the admittance (y), the impedance (z), the hybrid (h) and the inverse-hybrid (g) parameters, respectively. King Mongkut’s University of Technology Thonburi

  11. At port 1 At port 2 Open-circuit forward transimpedance Open-circuit input impedance Open-circuit output impedance Open-circuit reverse transimpedance EIE 211 Electronic Devices and Circuit Design II Two-Port Network (z-parameters) (Open-Circuit Impedance) King Mongkut’s University of Technology Thonburi

  12. EIE 211 Electronic Devices and Circuit Design II King Mongkut’s University of Technology Thonburi

  13. EIE 211 Electronic Devices and Circuit Design II Two-Port Network (y-parameters) (Short-Circuit Admittance) At port 1 At port 2 Short-circuit forward transadmittance Short-circuit input admittance Short-circuit output admittance Short-circuit reverse transadmittance King Mongkut’s University of Technology Thonburi

  14. EIE 211 Electronic Devices and Circuit Design II King Mongkut’s University of Technology Thonburi

  15. EIE 211 Electronic Devices and Circuit Design II Two-Port Network (h-parameters) (hybrid) At port 1 At port 2 Short-circuit forward current gain Short-circuit input impedance Open-circuit output admittance Open-circuit reverse voltage gain King Mongkut’s University of Technology Thonburi

  16. EIE 211 Electronic Devices and Circuit Design II King Mongkut’s University of Technology Thonburi

  17. EIE 211 Electronic Devices and Circuit Design II Two-Port Network (g-parameters) (inverse-hybrid) At port 1 At port 2 Open-circuit forward current gain Open-circuit input admittance Short-circuit output impedance Short-circuit reverse current gain King Mongkut’s University of Technology Thonburi

  18. EIE 211 Electronic Devices and Circuit Design II King Mongkut’s University of Technology Thonburi

  19. EIE 211 Electronic Devices and Circuit Design II z-parameter examples Note: (1) z-matrix in the last circuit = sum of two former z-matrices (2) z-parameters is normally used in analysis of series-series circuits (3) Z12 = Z21 (reciprocal circuit) (4) Z12 = Z21 and Z11 = Z22 (symmetrical and reciprocal circuit)

  20. EIE 211 Electronic Devices and Circuit Design II y-parameter examples King Mongkut’s University of Technology Thonburi

  21. EIE 211 Electronic Devices and Circuit Design II Example: figure below shows the small-signal equivalent-ckt model of a transistor. Calculate the values of the h parameters. King Mongkut’s University of Technology Thonburi

  22. EIE 211 Electronic Devices and Circuit Design II King Mongkut’s University of Technology Thonburi

  23. EIE 211 Electronic Devices and Circuit Design II Summary: Equivalent-Circuit Representation King Mongkut’s University of Technology Thonburi

  24. EIE 211 Electronic Devices and Circuit Design II Feedback King Mongkut’s University of Technology Thonburi

  25. Feedback Xs Xi Xo + - Xf βf What is feedback?Taking a portion of the signal arriving at the load and feeding it back to the input. What is negative feedback? Adding the feedback signal to the input so as to partially cancel the input signal to the amplifier. Doesn’t this reduce the gain? Yes, this is the price we pay for using feedback. Why use feedback?Provides a series of benefits, such as improved bandwidth, that outweigh the costs in lost gain and increased complexity in amplifier design. King Mongkut’s University of Technology Thonburi

  26. EIE 211 Electronic Devices and Circuit Design II Feedback Amplifier Analysis Xs Xi Xo + - Xf βf King Mongkut’s University of Technology Thonburi

  27. EIE 211 Electronic Devices and Circuit Design II Summary: General Feedback Structure A : Open Loop Gain A = Vo / V  : feedback factor  = Vf / Vo The product Aβ must be positive for the feedback network to be the negative feedback network. King Mongkut’s University of Technology Thonburi

  28. EIE 211 Electronic Devices and Circuit Design II Advantages of Negative Feedback • Gain desensitivity - less variation in amplifier gain with changes in β (current gain) of transistors due to dc bias, temperature, fabrication process variations, etc. • Bandwidth extension - extends dominant high and low frequency poles to higher and lower frequencies, respectively. • Noise reduction - improves signal-to-noise ratio • Improves amplifier linearity - reduces distortion in signal due to gain variations due to transistors • Impedance Control - control input and output impedances by applying appropriate feedback topologies • Cost of these advantages: • Loss of gain, may require an added gain stage to compensate. • Added complexity in design King Mongkut’s University of Technology Thonburi

  29. EIE 211 Electronic Devices and Circuit Design II Gain Desensitivity Feedback can be used to desensitize the closed-loop gain to variations in the basic amplifier. Let’s see how. • Assume βis constant. Taking differentials of the closed-loop gain equation gives… Divide by Af • This result shows the effects of variations in A on Af is mitigated by the feedback amount. 1+Aβ is also called the desensitivity amount We will see through examples that feedback also affects the input and resistance of the amplifier (increases Ri and decreases Ro by 1+Aβ factor) King Mongkut’s University of Technology Thonburi

  30. EIE 211 Electronic Devices and Circuit Design II Bandwidth Extension We’ve mentioned several times in the past that we can trade gain for bandwidth. Finally, we see how to do so with feedback… Consider an amplifier with a high-frequency response characterized by a single pole and the expression: • Apply negative feedback βand the resulting closed-loop gain is: • Notice that the midband gain reduces by (1+AMβ) while the 3-dB roll-off frequency increases by (1+AMβ) King Mongkut’s University of Technology Thonburi

  31. EIE 211 Electronic Devices and Circuit Design II Finding Loop Gain • Generally, we can find the loop gain with the following steps: • Break the feedback loop anywhere (at the output in the ex. below) • Zero out the input signal xs • Apply a test signal to the input of the feedback circuit • Solve for the resulting signal xo at the output • If xo is a voltage signal, xtst is a voltage and measure the open-circuit voltage • If xo is a current signal, xtst is a current and measure the short-circuit current • The negative sign comes from the fact that we are apply negative feedback King Mongkut’s University of Technology Thonburi

  32. EIE 211 Electronic Devices and Circuit Design II Basic Types of Feedback Amplifiers • There are four types of feedback amplifiers. Why? • Outputsampled can be a current or a voltage • Quantity fed back to input can be a current or a voltage • Four possible combinations of the type of output sampling and input feedback • One particular type of amplifier, e.g. voltage amplifier, current amplifier, etc. is used for each one of the four types of feedback amplifiers. • Feedback factor βf is a different type of quantity, e.g. voltage ratio, resistance, current ratio or conductance, for each feedback configuration. • Before analyzing the feedback amplifier’s performance, need to start by recognizing the type or configuration. • Terminology used to name types of feedback amplifier, e.g. Series-shunt • First term refers to nature of feedback connection at the input. • Second term refers to nature of sampling connection at the output. King Mongkut’s University of Technology Thonburi

  33. EIE 211 Electronic Devices and Circuit Design II Basic Feedback Topologies Depending on the input signal (voltage or current) to be amplified and form of the output (voltage or current), amplifiers can be classified into four categories. Depending on the amplifier category, one of four types of feedback structures should be used. (Type of Feedback)(Type of Sensing) (1) Series (Voltage) Shunt (Voltage) (2) Series (Voltage) Series (Current) (3) Shunt (Current) Shunt (Voltage) (4) Shunt (Current) Series (Current) King Mongkut’s University of Technology Thonburi

  34. EIE 211 Electronic Devices and Circuit Design II Figure 8.4 The four basic feedback topologies: (a) voltage-mixing voltage-sampling (series–shunt) topology; (b) current-mixing current-sampling (shunt–series) topology; (c) voltage-mixing current-sampling (series–series) topology; (d) current-mixing voltage-sampling (shunt–shunt) topology.

  35. EIE 211 Electronic Devices and Circuit Design II Basic Feedback Topologies series-shunt Depending on the input signal (voltage or current) to be amplified and form of the output (voltage or current), amplifiers can be classified into four categories. Depending on the amplifier category, one of four types of feedback structures should be used (series-shunt, series-series, shunt-shunt, or shunt-series) Voltage amplifier – voltage-controlled voltage source Requires high input impedance, low output impedance Use series-shunt feedback (voltage-voltage feedback) Current amplifier – current-controlled current source Use shunt-series feedback (current-current feedback) Transconductance amplifier – voltage-controlled current source Use series-series feedback (current-voltage feedback) Transimpedance amplifier – current-controlled voltage source Use shunt-shunt feedback (voltage-current feedback) shunt-series series-series shunt-shunt

  36. EIE 211 Electronic Devices and Circuit Design II Series-Shunt Feedback Amplifier - Ideal Case • Assumes feedback circuit does not load down the basic amplifier A, i.e. doesn’t change its characteristics • Doesn’t change gain A • Doesn’t change pole frequencies of basic amplifier A • Doesn’t change Ri and Ro • For the feedback amplifier as a whole, feedback does change the midband voltage gain from A to Af • Does change input resistance from Ri to Rif • Does change output resistance from Ro to Rof • Does change low and high frequency 3dB frequencies Basic Amplifier Feedback Circuit Equivalent Circuit for Feedback Amplifier

  37. EIE 211 Electronic Devices and Circuit Design II Series-Shunt Feedback Amplifier - Ideal Case Midband Gain Input Resistance Output Resistance It Vt King Mongkut’s University of Technology Thonburi

  38. EIE 211 Electronic Devices and Circuit Design II Series-Shunt Feedback Amplifier - Ideal Case Low Frequency Pole Low 3dB frequency lowered by feedback. High Frequency Pole Upper 3dB frequency raised by feedback. King Mongkut’s University of Technology Thonburi

  39. EIE 211 Electronic Devices and Circuit Design II Practical Feedback Networks • Feedback networks consist of a set of resistors • Simplest case (only case considered here) • In general, can include C’s and L’s (not considered here) • Transistors sometimes used (gives variable amount of feedback) (not considered here) • Feedback network needed to create Vf feedback signal at input (desirable) • Feedback network has parasitic (loading) effects including: • Feedback network loads down amplifier input • Adds a finite series resistance • Part of input signal Vs lost across this series resistance (undesirable), so Vi reduced • Feedback network loads down amplifier output • Adds a finite shunt resistance • Part of output current lost through this shunt resistance so not all output current delivered to load RL (undesirable) Vi Vo Vf • How do we take these loading effects into account? King Mongkut’s University of Technology Thonburi 39

  40. EIE 211 Electronic Devices and Circuit Design II Equivalent Network for Feedback Network • Need to find an equivalent network for the feedback network including feedback effect and loading effects. • Feedback network is a two port network (input and output ports) • Can represent with h-parameter network (This is the best for this particular feedback amplifier configuration) • h-parameter equivalent network has FOUR parameters • h-parameters relate input and output currents and voltages • Two parameters chosen as independent variables. For h-parameter network, these are input current I1 and output voltage V2 • Two equations relate other two quantities (output current I2 and input voltage V1) to these independent variables • Knowing I1 and V2, can calculate I2 and V1 if you know the h-parameter values • h-parameters can have units of ohms, 1/ohms or no units (depends on which parameter) King Mongkut’s University of Technology Thonburi

  41. EIE 211 Electronic Devices and Circuit Design II Series-Shunt Feedback Amplifier - Practical Case • Feedback network consists of a set of resistors • These resistors have loading effects on the basic amplifier, i.e they change its characteristics, such as the gain • Can use h-parameter equivalent circuit for feedback network • Feedback factor βf given by h12 since • Feedforward factor given by h21 (neglected) • h22 gives feedback network loading on output • h11 gives feedback network loading on input • Can incorporate loading effects in a modified basic amplifier. Basic gain of amplifier AV becomes a new, modified gain AV’ (incorporates loading effects). • Can then use feedback analysis from the ideal case. King Mongkut’s University of Technology Thonburi

  42. EIE 211 Electronic Devices and Circuit Design II Series-Shunt Feedback Amplifier - Practical Case Summary of Feedback Network Analysis • How do we determine the h-parameters for the feedback network? • For the input loading term h11 • Turn off the feedback signal by setting Vo = 0. • Then evaluate the resistance seen looking into port 1 of the feedback network (also called R11 here). • For the output loading term h22 • Open circuit the connection to the input so I1 = 0. • Find the resistance seen looking into port 2 of the feedback network (also called R22 here). • To obtain the feedback factor βf (also called h12 ) • Apply a test signal Vo’ to port 2 of the feedback network and evaluate the feedback voltage Vf (also called V1 here) for I1 = 0. • Find βf from βf = Vf/Vo’

  43. EIE 211 Electronic Devices and Circuit Design II Summary ofApproach to Analysis • Evaluate modified basic amplifier (including loading effects of feedback network) • Including h11 at input • Including h22 at output • Including loading effects of source resistance • Including load effects of load resistance • Analyze effects of idealized feedback networkusingfeedback amplifier equations derived • Note • Av’ is the modified voltage gain including the effects of h11 , h22 , RS and RL. • Ri’, Ro’ are the modified input and output resistances including the effects of h11 , h22 , RS and RL. Basic Amplifier Practical Feedback Network Modified Basic Amplifier Idealized Feedback Network King Mongkut’s University of Technology Thonburi

  44. EIE 211 Electronic Devices and Circuit Design II Example: Find expression for A, β, the closed-loop gain Vo/Vs, the input resistance Rin, and the output resistance Rout. Given μ = 104, Rid =100 kΩ, Ro = 1 kΩ, RL = 2 kΩ, R1 = 1 kΩ, R2 = 1MΩ and Rs = 10 kΩ. King Mongkut’s University of Technology Thonburi

  45. EIE 211 Electronic Devices and Circuit Design II King Mongkut’s University of Technology Thonburi

  46. EIE 211 Electronic Devices and Circuit Design II King Mongkut’s University of Technology Thonburi

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