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Announcements

Announcements. Troubles with Assignments… Assignments are 20% of the final grade Exam questions very similar ( 30% ) Deadline extended to 5pm Fridays, if you need it. Place in my mailbox (rm 217), or under my door (rm 222) Any later than that will not be graded

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Announcements

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  1. Announcements • Troubles with Assignments… • Assignments are 20% of the final grade • Exam questions very similar (30%) • Deadline extended to 5pm Fridays, if you need it. • Place in my mailbox (rm 217), or under my door (rm 222) • Any later than that will not be graded • Come and talk to me if you need help. • mid-term: Thursday, October 27th

  2. Adam Riess, Brian Schmidt and Saul Perlmutter

  3. Lecture 10 Overview • Transistors (continued) • The common-emitter amplifier • Amplifier parameters • Black box amplifier models

  4. Summary of useful equations • Basic DC operating conditions: • Add a small signal:

  5. Using small signal models e.g. Tmodel 1) Determine the DC operating conditions (in particular, the collector current, IC) 2) Calculate small signal model parameters: gm, rπ, re 3) Eliminate DC sources: replace voltage sources with shorts and current sources with open circuits 4) Replace BJT with equivalent small-signal model. Choose most convenient depending on surrounding circuitry 5) Analyze

  6. Voltage gain with small signal model ic + RC eliminate DC sources and apply T-model - vc ic + vbe re vbe - Find the gain using a small signal model:

  7. How to build a Real Common emitter amplifier • Why bother with 2 voltage supplies? • Use a voltage divider R2/R1 to provide base-emitter voltage to correctly bias the transistor.

  8. DC condition: the voltage divider • The voltage divider should provide sufficient voltage to place the transistor in active mode (base-emitter forward biased): • Current through resistors should be >10 times base current for stability

  9. Amplifier specifications • What other parameters of an amplifier do we care about? • Voltage gain • Dynamic range • Frequency response (bandwidth) • Input impedance • output impedance

  10. Voltage Gain • Voltage gain • Use small signal model (short Voltage sources and capacitors) ground αie voltage gain usually re<<RE • Voltage gain is only defined by resistors RC and RE ground

  11. Frequency response (Bandwidth) • Normally interested in providing a small, AC signal to the base • Use capacitors to remove ("block") any low frequency (DC) component ("capacitively couple the signal to the base") which could affect the bias condition • C1 forms a high-pass filter with R1in parallel with R2 (Assuming the AC impedance into the base is large). • Cut off frequency ω0=1/RC, so to remove frequencies <fmin:

  12. Frequency response (Bandwidth) • Also worthwhile to place a capacitor on the output • C2 forms a high pass filter with RL. • Cut off frequency ω0=1/RC, so to remove frequencies <fmin:

  13. Dynamic Range • Maximum voltage output = Vbb • Minimum = 0 • Beyond this the signal becomes 'clipped' or distorted • To get the maximum possible voltage swing, both positive and negative, set VC=0.5 VBB • Maximum 'dynamic range' VC

  14. rOUT rb Input impedance • Consider the circuit without the voltage divider resistors. What's the small signal (AC) input impedance at the base, rb? • Including voltage divider resistors in parallel • Input signal sees a total input impedance rIN= R1 // R2 // rb RB

  15. ROUT rb Output impedance

  16. If RL=10kΩ and we want a low frequency cutoff of 20Hz, What is C2? • If VBB=15V and IC=2mA what is the output impedance? DC condition Frequency response Gain/Dynamic range Impedance

  17. Impedances • Why do we care about the input and output impedance? • Simplest "black box" amplifier model: ROUT VOUT VIN RIN AVIN • The amplifier measures voltage across RIN, then generates a voltage which is larger by a factor A • This voltage generator, in series with the output resistance ROUT, is connected to the output port. • A should be a constant (i.e. gain is linear)

  18. Impedances • Attach an input - a source voltage VS plus source impedance RS RS ROUT RIN VOUT AVIN VIN VS • Note the voltage divider RS + RIN. • VIN=VS(RIN/(RIN+RS) • We want VIN = VS regardless of source impedance • So want RIN to be large. • The ideal amplifier has an infinite input impedance

  19. Impedances • Attach a load - an output circuit with a resistance RL RS ROUT RL RIN AVIN VIN VOUT VS • Note the voltage divider ROUT + RL. • VOUT=AVIN(RL/(RL+ROUT) • Want VOUT=AVIN regardless of load • We want ROUT to be small. • The ideal amplifier has zero output impedance

  20. Operational Amplifier • Integrated circuit containing ~20 transistors

  21. Operational Amplifier • An op amp is a high voltage gain amplifier with high input impedance, low output impedance, and differential inputs. • Positive input at the non-inverting input produces positive output, positive input at the inverting input produces negative output. • Can model any amplifier as a "black-box" with a parallel input impedance Rin, and a voltage source with gain Av in series with an output impedance Rout.

  22. RS + RL vout - Ideal op-amp • Place a source and a load on the model So the equivalent circuit of an ideal op-amp looks like this: • Infinite internal resistance Rin (so vin=vs). • Zero output resistance Rout (so vout=Avvin). • "A" very large • No saturation • iin=0; no current flow into op-amp

  23. Schematics • An amplifier will not work without a power supply. And a more complete diagram looks like the figure below, which also indicates the standard pin configuration.

  24. Measuring Impedances RS ROUT RL RIN AVIN VIN VOUT VS • Assuming you can only vary RL and RS, how would you measure the input and output impedances of the amplifier?

  25. Measuring Impedances RS ROUT RL RIN AVIN VIN VOUT VS • With the black box model, it is simple to measure the input and output impedances of an amplifier • To measure the input impedance, vary RS until the output voltage has dropped to half ; then RS=RIN= input impedance • To measure the output impedance, vary RL until the output voltage has dropped to half ; then RL=ROUT= output impedance

  26. Cascaded Amplifiers • Easiest way to increase amplification is to link amplifiers together ROUT1 ROUT2 A2 VIN2 A1VIN1 VOUT2 VOUT1 RIN2 RIN1 VIN1 VIN2 • Ideal amplifiers; VOUT2=A1A2VIN1 • In reality, take account of voltage divider action due to input and output impedances

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