=

1

F f = 0

1 +

RF

RIN

fz =

1

2S Rc + RIN || RF)C

fp =

1

2SRcC

=

1

F

¨

¨

©

§

1 +

RF

RIN ¨

¨

©

§1 + s(R

c + RIN || RF) C

1 + sRcC

VOUT

VIN

=

1

F

VOUT

VIN

=

A

1 + AF

F =

VA - VB

VOUT

LMP7717

RIN

RC

C

RF

LMP7717, LMP7718

www.ti.com

SNOSAY7H – MARCH 2007 – REVISED MARCH 2013

Input Lead-Lag Compensation

The recommended technique which allows the user to compensate the LMP7717/LMP7718 for stable operation

at any gain is lead-lag compensation. The compensation components added to the circuit allow the user to shape

the feedback function to make sure there is sufficient phase margin when the loop gain is as low as 0 dB and still

maintain the advantages over the unity gain op amp. Figure 49 shows the lead-lag configuration. Only RC and C

are added for the necessary compensation.

Figure 49. LMP7717 with Lead-Lag Compensation for Inverting Configuration

To cover how to calculate the compensation network values it is necessary to introduce the term called the

feedback factor or F. The feedback factor F is the feedback voltage VA-VB across the op amp input terminals

relative to the op amp output voltage VOUT.

(1)

From feedback theory the classic form of the feedback equation for op amps is:

(2)

A is the open loop gain of the amplifier and AF is the loop gain. Both are highly important in analyzing op amps.

Normally AF >>1 and so the above equation reduces to:

(3)

Deriving the equations for the lead-lag compensation is beyond the scope of this datasheet. The derivation is

based on the feedback equations that have just been covered. The inverse of feedback factor for the circuit in

Figure 49 is:

(4)

where 1/F's pole is located at

(5)

1/F's zero is located at

(6)

(7)

The circuit gain for Figure 49 at low frequencies is

−RF/RIN, but F, the feedback factor is not equal to the circuit

gain. The feedback factor is derived from feedback theory and is the same for both inverting and non-inverting

configurations. Yes, the feedback factor at low frequencies is equal to the gain for the non-inverting configuration.

Copyright © 2007–2013, Texas Instruments Incorporated

Submit Documentation Feedback

17

Product Folder Links: LMP7717 LMP7718