Analog Integrated Circuits Fundamental Building Blocks Fundamental - PowerPoint PPT Presentation

Analog Integrated Circuits Fundamental Building Blocks Fundamental Building Blocks Basic OTA/Opamp architectures Faculty of Electronics Telecommunications and Information Technology Information Technology Gabor Csipkes Bases of Electronics Department

Outline  definition of the OTA/opamp  cascade of amplifier stages – the general opamp architecture  the uncompensated Miller opamp – small signal model at low and high frequencies  the uncompensated Miller opamp – small signal model at low and high frequencies  step response of a second order system with unity feedback  the two stage opamp with Miller compensation – models and parameters  sizing algorithm for the two stage Miller opamp  the telescopic opamp – voltage budget, models and parameters  sizing algorithm of the telescopic opamp  the folded cascode opamp – small signal low and high frequency model  sizing algorithm for the folded cascode opamp Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 2

The ideal opamp - definitions  ideal opamp = a differential input, voltage controlled voltage source with very large open loop gain  the ideal gain is frequency independent, but real gain can be modeled with a set of poles and zeros → typically low pass behavior  very large input resistance and near zero output resistance  opamps with strictly capacitive loads can have large output resistance → Operational Transconductance Amplifiers (OTA) often also called opamp  the output may be single ended (referenced to ground) or differential  single or symmetrical supply voltages       V a V V out Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 3

The opamp – a cascade of elementary stages  the typical opamp architecture → a differential amplifier followed by a high gain inverting stage and a voltage follower for low output impedance  the voltage follower may be missing if the load is known to be strictly capacitive  frequency compensation for closed loop stability probably required (more on this later)  frequency compensation for closed loop stability probably required (more on this later)  elementary amplifier stages → subsequent V -I and I-V conversions  most simple form → the two stage opamp V-I I-V I-V I-V cascade of elementary stages V-I Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 4

The two stage or Miller opamp Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 5

The two stage opamp  the small signal low frequency model with two equivalent stages  no capacitive effects → low frequency or DC voltage gain  each stage can be analyzed individually → G m and R out specific to each configuration V     G G g g m m 1 1 m m 1,2 1,2    a G R G R   R r || r         0 m 1 out 1 m 2 out 2 out 1 DS 2 DS 4  a a  G g 1 2  m 2 m 6   R r || r  out 2 DS 6 DS 7 Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 6

The two stage opamp  the small signal high frequency model → consider load and parasitic capacitances    C C C 1 2 GD 1,2      C C C C C  3 GS 3 GS 4 DB 1 DB 3 V V     C C C C   4 GD 4     C C C C  5 GS 6 DB 2 DB 4   C C  6 GD 6      C C C C C  7 L DB 6 DB 7 L a  a s ( ) 0           1 1 sR sR C C 1 1 sR sR C C out out 1 1 5 5 out out 2 2 7 7 The frequency response is dominated by C 5 and C 7 due to the large R out 1 and R out 2 ! Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 7

The two stage opamp – with negative feedback  the closed loop model of an opamp with negative feedback a   a s ( ) 0 a s ( )     A s ( ) s s     1  1  1 a s ( ) r                 p 1 p 2 a       0 1 a r  p 1 p 2 0 a s ( ) 1 a r   A s ( ) 0 The closed loop gain:               1 a s ( ) r 2 s s 1 a r p 1 p 2 p 1 p 2 0     2 A A The standard form of a second order transfer function: The standard form of a second order transfer function:   A s A s ( ) ( ) 0 0 n n (DC gain A 0 , resonant frequency ω n and damping factor ξ )     2 2 s 2 s n n    a 1            p 1 p 2 A 0 ; 1 a r ;   0 n p 1 p 2 0  1 a r r    2 1 a r 0 p 1 p 2 0 Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 8

Frequency response of a second order system  the effect of the feedback transmittance r on the magnitude response   1  A 0 r A 0 decreases with r  Overshoot of the frequency response at ω n → complex poles → under damped step response  worst case stability for unity gain ( r =1 and A 0 =1) → lowest ξ for given a 0 , ω p 1 and ω p 2 Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 9

Step response for unity gain feedback    A s ( ) L  1 V ( ) t  the time domain step response is calculated as   out   s  damping of the oscillation amplitude depends on ξ  typically, if poles ω p 1 and ω p 2 are close to each other ξ <1 → under damped system with fading oscillations of the step response fading oscillations of the step response           n t 2 1 e            2 V ( ) t 1 sin 1 t arctan   out  n     2 1         fading exponential fading exponential oscillations with the period oscillations with the period envelope depending on ω n and ξ  since the sin function varies between - 1 and 1 → time domain overshoot around the unit step → the overshoot and number of cycles until settling increases with a smaller ξ Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 10

Step response for unity gain feedback  step response of the two stage opamp in unity gain feedback configuration   optimal optimal response      the circuit is unusable as amplifier for small ξ due to the very long settling time  the response stability depends on the phase margin ( m φ ) → optimal response for m φ =65° Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 11

Stability and phase margin a s ( )   A s ( )  closed loop gain for unity feedback: What if denominator is 0 ??? 1 a s ( ) a s   ( ) 1  the closed loop gain approaches ∞ → even for no input any perturbation is amplified with under damped transients → sustained oscillations occur, feedback turns positive and with under damped transients → sustained oscillations occur, feedback turns positive and system becomes unstable    a j ( ) 1   Barkhausen's stability criteria:         a j ( ) 180 a 0 solve for ω       f 1   0 dB  1 j  1 j                  p p 1 1 p p 2 2       m 180  a j  odB              180 arctan 0 dB arctan 0 dB           p 1 p 2 Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 12

Pole locations and phase margin  the relation between pole frequencies and f 0 dB defines m φ and the stability of the step response This is what we need ! we need !    f f f f f f p 2 0 dB p 2 0 dB p 2 0 dB       m  45 m  45 m  45 Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 13

Frequency compensation  need f p 2 > f 0 dB so that m φ >45° → impossible to achieve by simply cascading a differential amplifier and a common source inverting amplifier Typically:  1  f     p p 1 1     R R R R 2 2 R R C C   out 1 out 2 out 1 5    C C 1    7 5 f  p 2  2 R C  out 2 7 f p 1 and f p 2 are close to each other !!! We need to manipulate pole locations to separate f p 1 and f p 2 → → frequency compensation Analog Integrated Circuits – Fundamental building blocks – Basic OTA/Opamp architectures 14