EE124 Lab Experiment 5 Design of a Feedback Circuit 16. March 2005 Udo Strasilla & Cuong Nguyen Feedback Theory Vio Definitions: Vo Open loop gain: A= Vio Loop gain : Make Vi = 0 Open the loop at a convenient place, for example at Vio. Apply a test signal Vt there. Then LG =(βAVt) / Vt = -Aβ Vo Closed Loop gain: Af = =A / (1+Aβ) ; If Aβ >> 1, then Af≈1/β Vi Advantage: Af depends mostly on the β network, thus is less-sensitive to variations of the open loop amplifier characteristics. Other advantage : Dependent on the feedback configuration the input and the output resistance may be increased and/or decreased, respectively. To obtain a deeper understanding of feedback theory you should study the feedback portion of Sedra/Smith, MicroelectronicCircuits. a) Fifth Edition: pp. 799 – 831 (The most important part pertaining to Lab 5 would be on pp. 799 – 810 and on page 830). b) Fourth Edition: pp. 675 – 709 (The most important part pertaining to Lab 5 would be on pp. 675 – 688 and on page 709). Only two feedback configurations are shown below. The designer should know that in feedback circuits the relative high open loop gain is traded into a lower closed loop gain. The “payback” is that the input impedance and/or output impedance of the open loop amplifier may be altered depending on the feedback configuration used. If you wish to increase the existing open loop amplifier input resistance then you must choose a series-input (voltage combining) configuration. If you wish to decrease the existing open loop amplifier output resistance then you must choose a shunt-output (voltage sampling) configuration. Examples of Feedback configurations: Effect on The Lab 5 Experiment In the Lab 5 experiment the transconductance amplifier characterized in Lab 4 is used as an open loop amplifier. A circuit has to be designed such as to meet one of a set of three specifications given in the Appendix of the EE124 Lab Manual. The specifications of the feedback amplifier call for a reduced gain Af, an increasedinput resistance Rif, and a decreased output resistance Rof. Thus it is obvious that only a series-shunt feedback configuration will do this job. This decision has been done for you already in the lab manual by suggesting the circuit where the feedback output (left side of the beta-network) is in series with the input to the open loop amplifier, and where the feedback circuit input (right side of the beta-network) is in shunt with the load resistor RL. Let us consider an example, where the spec’s to be achieved are in the left column of the following table, and where the measured properties of the open loop amplifier are in the right column. Note: your values will be different dependent on your specification and on the values measured in Experiment 4. Closed Loop Amplifier Specification Open Loop Amplifier: Measured Example properties RL = 10 k A = 190 V/V Af = 5 ± 10 % Rid = 18 kOhm Rof ≤ 750 Ω Ro = 50 kOhm Rif ≥ 330 k Note: Before you trust your measured data of Expt 4, you should verify the validity of your measurements by using your understanding of the model of the transconductance amplifier. A = GMRL=gmRL=(Ic/Vt)RL=(Ibias/2Vt)RL. Assuming Ibias = 1mA and RL=10kOhm, we get A=(1m/(2*25m))*10k=200V/V. It looks like our predicted gain is fairly close to the measured gain in above table. Rid ≈ * 2 rπ= * 2 ( β+ 1)* r = * 2 ( β+ 1)* V / I = * 2 ( β+ 1) 2 * V / I e te tbias Assuming β= 100 , we get Rid=2*101*50m/1m=10.1 kOhm. It looks like the measured Rid is almost a factor of two higher than our predicted Rid. The reason for this discrepancy is that our β -assumption is too low. More likely the actual device beta is almost a factor of two higher. In Lab 4 we “measured” the beta indirectly by measuring the base current Ibase, and then using the formula IC β= , where Ic=Ibias/2. Thus we don’t have to guess the beta in order toBase calculate the expected Rin. Ro ≈ ro , since we are looking into the collector of two parallel transistors from the 2 output node in the transconductance amplifier of Expt. 4. Though we didn’t make any measurement of the Early resistance of the transistors within the transconductance amplifier, we may assume that ro is similar as that of the current mirror of Experiment 1. Thus let us use ro=100 kOhm, resulting in Ro=50kOhm. Analysis of the Feedback Circuit of Expt. 5 Initial Circuit Model: To use the Rof formula (Rof = Ro / (1 + Aβ) ) you need to idealize the β network. This is done in two steps: 1. 1. Convert above β- network into a network where you have a series resistor on the left and a shunt resistor on the right. This may be achieved by using the h-parameter representation of the β-network. 2. 2. Idealize the β network by moving the resistors into the amplifier above. R1//R2 is moved by sliding the resistor combination along the input wire. R1 + R2 is moved by sliding the resistors between the two output wires. Modified β net work Idealized β net workRedraw the total circuit with the idealized β network. Since we modified the original open amplifier, we rename it the “Modified Amplifier”. Ro mod To apply the simplified feedback formulas, you need to re-calculate the parameters of the modified amplifier Vo Amod = , where Vimod is the input voltage to the modified amplifier. Vimod Vo = GMVid ( ro // (R1+R2)// RL ) 2 Assume ro >> (R1+R2)// RL 2 Substitute R22 = R1 + R2 RLR22 Then Vo = GM Vid RL + R22Rid But Vid = Vimod Rid + R3 + R// 1 R2 Purpose of R3 : To balance the offset voltage caused by R1//R2. Therefore, make R3 = R1 // R2 Thus Rid RLR22 Amod = GM ; where R22 = R1 + R2 and R3 = R1// R2 Rid + 2R3 RL + R22 Ro mod = R1 + R2 = R22 Ri mod = Rid + R3 +R1 // R2 = Rid + 2R3 R1 β = R1 + R2 Now finally you can apply the feedback equations: Af = Amod / (1 + Amod β)= 5 Rof = Ro mod / (1+Amod β) ≤ 750 Ω Rif = Rimod (1 + Amod β) ≥ 330 kΩ Finding R1 and R2 To meet the design goal, above equations and inequalities have to be satisfied. The only real unknowns are R1 and R2. In the initial stage you may reduce your problem to one unknown, either R1 or R2, by taking advantage of the approximation: Af ≈ 1/ β . Assume you choose R1 to be the unknown. Make an educated guess of the value for that unknown and run through all the equations, to see which equation and/or inequality