1. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Chapter 11: BJT and JFET Frequency Response

2. Slide 1 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. General Frequency Considerations Frequency response of an amplifier refers to the frequency range in which the amplifier will operate with negligible effects from capacitors and capacitance in devices. This range of frequencies can be called the mid-range. At frequencies above and below the midrange, capacitance and any inductance will affect the gain of the amplifier. At low frequencies the coupling and bypass capacitors will lower the gain. At high frequencies stray capacitances associated with the active device will lower the gain. Also cascading amplifiers will limit the gain at high and low frequencies.

3. Slide 2 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Bode Plot A Bode plot indicates the frequency response of an amplifier. The horizontal scale indicates the frequency (in Hz) and the vertical scale indicates the gain (in dB).

4. Slide 3 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Cutoff Frequencies The mid-range frequency of an amplifier is called the Bandwidth of the amplifier. The Bandwidth is defined by the Lower and Upper Cutoff frequencies. Cutoff: frequency at which the gain has dropped by: 0.5 power 0.707 voltage -3dB

5. Slide 4 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Low Frequency Response – BJT Amplifier At low frequencies Coupling capacitors (C s, C C ) and Bypass capacitors (C E ) will have capacitive reactances (X C ) that affect the circuit impedances.

6. Slide 5 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Coupling Capacitor - CS The cutoff frequency due to CS can be calculated: [Formula 11.27] using [Formula 11.29]

7. Slide 6 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Coupling Capacitor - CC The cutoff frequency due to CC can be calculated: [Formula 11.31] using [Formula 11.32]

8. Slide 7 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Bypass Capacitor - C E The cutoff frequency due to CE can be calculated: [Formula 11.33] using [Formula 11.34] where

9. Slide 8 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Bode Plot of Low Frequency Response – BJT Amplifier The Bode plot indicates that each capacitor may have a different cutoff frequency. It is the device that has the highest lower cutoff frequency (f L ) that dominates the overall frequency response of the amplifier.

10. Slide 9 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Roll-off of Gain in the Bode Plot The Bode plot not only indicates the cutoff frequencies of the various capacitors it also indicates the amount of attenuation (loss in gain) at these frequencies. The amount of attenuation is sometimes referred to as roll-off. The roll-off is described as dB loss-per-octave or dB loss-per-decade.

11. Slide 10 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. -dB/Decade -dB/Decade refers to the attenuation for every 10-fold change in frequency. For Low Frequency Response attenuations it refers to the loss in gain from the lower cutoff frequency to a frequency 1/10th the lower cutoff frequency. In the above drawn example: fLS = 9kHz gain is 0dB fLS/10 =.9kHz gain is –20dB Therefore the roll-off is 20dB/decade. The gain decreases by –20dB/Decade.

12. Slide 11 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. -dB/Octave -dB/Octave refers to the attenuation for every 2-fold change in frequency. For Low Frequency Response attenuations it refers to the loss in gain from the lower cutoff frequency to a frequency 1/2 the lower cutoff frequency. In the above drawn example: fLS = 9kHz gain is 0dB fLS/2 = 4.5kHz gain is –6dB Therefore the roll-off is 6dB/octave. This is a little difficult to see on this graph because the horizontal scale is a logarithmic scale.

13. Slide 12 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Low Frequency Response – FET Amplifier At low frequencies Coupling capacitors (CG, CC) and Bypass capacitors (CS) will have capacitive reactances (XC) that affect the circuit impedances.

14. Slide 13 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Coupling Capacitor - CG The cutoff frequency due to CG can be calculated: [Formula 11.35] using [Formula 11.36]

15. Slide 14 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Coupling Capacitor - CC The cutoff frequency due to CC can be calculated: [Formula 11.37] using [Formula 11.38]

16. Slide 15 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Bypass Capacitor - CS The cutoff frequency due to CS can be calculated: [Formula 11.39] using [Formula 11.41]

17. Slide 16 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Bode Plot of Low Frequency Response – FET Amplifier The Bode plot indicates that each capacitor may have a different cutoff frequency. The capacitor that has the highest lower cutoff frequency (f L ) is closest to the actual cutoff frequency of the amplifier.

18. Slide 17 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Miller Effect Capacitance Any P-N junction can develop capacitance. This was mentioned in the chapter on diodes. In a BJT amplifier this capacitance becomes noticeable between: the Base-Collector junction at high frequencies in CE BJT amplifier configurations and the Gate-Drain junction at high frequencies in CS FET amplifier configurations. It is called the Miller Capacitance. It effects the input and output circuits.

19. Slide 18 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Miller Input Capacitance (C Mi ) It can be calculated: [Formula 11.42] Note that the amount of Miller Capacitance is dependent on interelectrode capacitance from input to output (C f ) and the gain (Av).

20. Slide 19 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Miller Output Capacitance (C Mo ) It can be calculated: [Formula 11.43] If the gain (Av) is considerably greater than 1: [Formula 11.44]

21. Slide 20 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. High-Frequency Response – BJT Amplifiers Capacitances that will affect the high-frequency response: Cbe, Cbc, Cce – junction capacitances Cwi, Cwo – wiring capacitances CS, CC – coupling capacitors CE – bypass capacitor

22. Slide 21 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. High-Frequency Cutoff – Input Network (f Hi ) [Formula 11.46] using [Formula 11.47] and [Formula 11.48]

23. Slide 22 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. High-Frequency Cutoff – Output Network (f Ho ) [Formula 11.49] using [Formula 11.50] and [Formula 11.51]

24. Slide 23 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. hfe (or  ) Variation The hfe parameter (or  ) of a transistor varies with frequency. [Formula 11.55]

25. Slide 24 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Full Frequency Response of a BJT Amplifier Note the highest Lower Cutoff Frequency (f L ) and the lowest Upper Cutoff Frequency (f H ) are closest to the actual response of the amplifier.

26. Slide 25 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. High-Frequency Response – FET Amplifier Capacitances that will affect the high-frequency response: Cgs, Cgd, Cds – junction capacitances Cwi, Cwo – wiring capacitances CG, CC – coupling capacitors CS – bypass capacitor

27. Slide 26 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. High-Frequency Cutoff – Input Network (f Hi ) [Formula 11.61] using [Formula 11.62] and [Formula 11.63] [Formula 11.64]

28. Slide 27 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. High-Frequency Cutoff – Output Network (f Ho ) [Formula 11.65] using [Formula 11.66] and [Formula 11.67]

29. Slide 28 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Multistage Frequency Effects Each stage will have its own frequency response. But the output of one stage will be affected by capacitances in the subsequent stage. This is especially so when determining the high frequency response. For example, the output capacitance (C o ) will be affected by the input Miller Capacitance (C Mi ) of the next stage.

30. Slide 29 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Total Frequency Response of a Multistage Amplifier Once the cutoff frequencies have been determined for each stage (taking into account the shared capacitances), they can be plotted. Again note the highest Lower Cutoff Frequency (f L ) and the lowest Upper Cutoff Frequency (f H ) are closest to the actual response of the amplifier.

31. Slide 30 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Square Wave Testing In order to determine the frequency response of an amplifier by experimentation, you must apply a wide range of frequencies to the amplifier. One way to accomplish this is to apply a square wave. A square wave consists of multiple frequencies (by Fourier Analysis: it consists of odd harmonics).

32. Slide 31 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Square Wave Response Waveforms If the output of the amplifier is not a perfect square wave then the amplifier is ‘cutting’ off certain frequency components of the square wave.