11. Active Filters and Tuned Circuits. 11. Active Filters and Tuned Circuits TLT-8016 Basic Analog Circuits 2005/2006 1

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1 . Active Filters and Tuned ircuits. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6

2 . Active ow - Pass Filters Active ilters: circuits, containing resistors, capacitors and Op Amps. They are intended or separating o signals having dierent requencies. equirements or ilters:. ontain ew components.. Have a transer unction that is insensitive to component tolerances.. Place modest demands on the op amp s gainbandwidth product, output impedance, slew rate, and other speciications. 4. Be easily adusted. 5. equire a small spread o component values. 6. Allow a wide o useul transer unctions to be realized. Butterworth Transer Function H ( ) H (.) + ( / ) n b break (cut-o) requency. Figure. Transer unction magnitude versus requency or low-pass Butterworth ilters. b. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6

3 Sallen - Key ircuits Figure. Equal-component Sallen-Key low-pass active-ilter section. b (.) π. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6

4 Example. Fourth - Order ow - Pass Butterworth Filter Design Design a ourth - order low - pass Butterworth ilter with a cut - o requency o Hz. Use the F4 op amp. Solution: We choose.µf and rom (.) π π. 6 b From table. K.5; K.5. We choose 4 4 kω and ( K ) 4 (.5 ).5kΩ ( K ) (.5 ).5kΩ 4 5.8kΩ Figure. Fourth-order Butterworth low-pass ilter.. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6 4

5 Transormation o low-pass transer unction to high-pass transer unction: b /. H hp ( ) ( / ) n b. Active High - Pass Filters H (.) + Figure.8 Sallen-Key high-pass active-ilter section. Figure.7 Normalized high-pass Butterworth transer unctions. Figure.9 Bode magnitude plot or the high-pass ilter.. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6 5

6 . Active Bandpass Filters Delyiannis - Friend Bandpass ircuits (.6) π ( ) H (.7) B (.8) π Q B / (.9) Q (.) π H 4Q H (.) (.) Figure. Second-order bandpass ilter.. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6 6

7 Example. Bandpass Filter Design Design a bandpass ilter with khz, B Hz, and H. Solution: Q B ( ) 5 Q. 59 (.) π (.4) H must be large to have high input impedance. From (.4) and must have moderate value to keep the value o realistic. The choice kω gives kω.5kω 7.96nF We select 8.nF and then calculate again the values o, and. (.5) 4Q H 8 Figure. Bandpass ilter designed in Example... Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6 7

8 .4 The Series esonant ircuit esonant Frequency and Quality Factor A v ( ) Figure.7 Series resonant circuit. I o + / i ( ) + o I i + + / o i + + / (.6) (.7) (.8) (.9) esonant requency Quality actor At the resonance (.) (.) π Q (.) (.) Another ormula or the quality actor Q (.4). Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6 8

9 oltage transer ratio, expressed with Q-actor and resonant requency ( ) ( / ) ( / ) [ ] ( / ) A v (.5) Q + A v i ; A v when. For requencies between and A v > and has a maximum at. The circuit is a bandpass ilter. Figure.8 oltage transer unction or the series resonant circuit.. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6 9

10 ircuit Bandwidth B H H Q (.8) (.9) I B is relatively small, compared with, then B / (.) H + B / (.) Figure.9 Normalized impedance o the series resonant circuit. Figure. Bandwidth and hal-power requencies or the series resonant circuit.. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6

11 Exercise.7 Find resonant requency, Q, the bandwidth, and hal - power requencies o a series resonance circuit having 5 µh, pf, and Ω. Solution: π π 5 B 6 7. B π π 7. 5 Q 6 7. B 8kHz Q.4 H MHz 6.96MHz 7.8MHz. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6

12 .5 The Parallel esonant ircuit Q (.5) Z ( ) Figure.5 Parallel resonant circuit. / + / ( ) + (.) Z ( ) ( / ) ( / ) + [ ] ( / ) (.6) Q B H Q H π (.) B Q (.4) / H + B /. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6

13 Figure.6 Normalized impedance o the parallel resonant circuit.. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6

14 .8 Tuned Ampliiers Tuned ampliiers have resonant circuits at their inputs or outputs or both and they ampliy in a narrow bandwidth. Figure.4 Tuned ampliier. o ( ) gmgsz (.57) A v o gmz( ) (.58) in. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6 4

15 Input Impedance Neutralization Figure.47 Parallel input resistance and reactance or the tuned ampliier o Figure.44. Pay attention to the negative real part at requencies below the resonant requency. Figure.48 neut is used to cancel the eedback through gd.. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6 5

16 .9 Oscillators The Hartley Oscillators Figure.5 Hartley oscillator.. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6 6

17 . Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6 7 Frequency o Oscillation and the Minimum Transconductance equirement (.6) ( ) + + g m (.6) (.6) and (.6) orm a homogeneous set o linear equations concerning and. The solution is nonzero i the system determinant is zero: ( ) ( ) + g m (.64) Figure.5 Hartley oscillator. ( ) + (.6) m g (.66) ( ) g m (.6)

18 + + + gm (.66) From zeroing o the real part o (.66): (.68) + ( ) From zeroing o the imaginary part o (.66): g m (.7). Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6 8

19 The Piezoelectric Eect. rystal - ontrolled Oscillators Piezoelectric eect: i we apply an electric ield to the plates, orces on the ions in the lattice deorm the material. Piezoelectric eect is reciprocal: i deorm the crystal, a voltage appears between the plates. When used as requency-determining element, quartz crystal vibrates reely at the desired requency. The mechanical vibrations result in an ac current in the external circuit. Figure.54 rystal.. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6 9

20 The Equivalent ircuit o the rystal Table. Parameters o a typical -MHz rystal. Figure.56 Equivalent circuit or a crystal.. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6

21 Figure.57 rystal reactance versus requency.. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6

22 rystal Oscillator ircuits Figure.5a olpitts oscillator. Figure.58 Pierce oscillator results rom the olpitts oscillator (Figure.5) i the inductor is replaced by a crystal. The dc blocking capacitor shown in Figure.5 can be omitted because the crystal is an open circuit or dc.. Active Filters and Tuned ircuits TT-86 Basic Analog ircuits 5/6