LINEAR TECHNOLOGY LT5400 Technical data

Matched Resistor Networks for Precision Amplifi er Applications

Design Note 502

Tyler Hutchison

Introduction

Some ideal op amp confi gurations assume that the
feedback resis tors exhibit perfec t matching. In practice,
resistor non-idealities can af fect various circuit param­eters such as common mode rejection ratio (CMRR),
harmonic distortion and stability. For instance, as
shown in Figure 1, a single-ended amplifi er confi gured
to level-shift a ground-referenced signal to a common
mode of 2.5V needs a good CMRR. Assuming 34dB
CMRR and no input signal, this 2.5V level shi fter exhibits
an output offset of 50mV, which can even overwhelm
the LSB and offset errors of 12-bit ADCs and drivers.

R

V

–

LTC6255

+

CC

+

DN502 F01

–

V

EE

R

+

V

IN

–

R

2.5V

+

R

–

DC

Figure 1. A Single-Ended Op Amp Used as a Level Shifter

For an op amp, 34dB is a less than ide al CMRR. However,
a feedback network of 1% tolerance resistors can limit
the CMRR to 34dB regardless of the op amp’s capabili­ties. Highly matched resistors, such as those provided

®

by the LT

5400, available in 0.01%, 0.025% and 0.05%
matching, ensure that the designer can approach or
meet amplifi er data sheet specifi cations. This design
note compares the LT5400 with thick fi lm, 0402, 1%
tolerance surface mount resistors. CMRR, harmonic
distortion and stability are considered with these resis­tors for feedback around an LTC6362 op amp, as shown
in Figure 2.

Common Mode Rejection Ratio

In order to obtain precis e measurements in the presence
of common mode noise, a high CMRR is important.
Input CMRR is defi ned as the ratio of differential gain
(V

OUT(DIFF)/VIN(DIFF)

differential conversion (V

) to the input common mode to

OUT(DIFF)/VIN(CM)

).

R2
1k

–

LTC6362

+

5V

+

–

R3
1k

50Ω

50Ω

3.3nF

3.3nF

3.3nF

DN502 F02

+

A

IN

TO ADC

–

A

IN

R1
5k

+V

IN

R4
5k

–V

IN

Figure 2. Fully Differential Op Amp Confi gured for
V

OUT/VIN

= 0.2

In ideal single-ended and fully differential amplifi ers,
only the input differential level affects the output volt­age. However, in real circuits, resistor mismatch limits
the available CMRR. Consider this circuit confi gured to
attenu ate a ±10V signal to a ±2V signal. Using t ypical sur­face mount resistors with 2% matching (1% tolerance),
the worst-case CMRR contribution from the resistors
is 30dB. With 0.01% tolerance, 0.02% matching, the
worst-case CMRR contribution from the resistors is
70dB. A limiting factor in the CMRR equation is:

R3

⎛
⎜

⎝

R2

R2

⎞

–

⎟

⎠

R4

R1

12R1

This expression r educes to the resistor matching r atio for
typic al resistors, but the LT5400 t akes an additional step
to offer improved CMRR by constraining the matching
between resistor pairs R1/R2 and R4/R3. By defi ning
this equation as matching for CMRR, the LT5400 offers
accuracy that’s better than just the resistor matching
ratio. For example, the LT5400A guarantees:

∆R

⎛

⎞

⎜

⎟

⎝

⎠

R

≤0.005%

CMRR

which improves worst-case CMRR to 82dB.

L, LT, LTC, LTM, Linear Technology and the Linear logo are registered trademarks
of Linear Technology Corporation. All other trademarks are the property of their
respective owners.

05/12/502

A bench test of the circuit yielded a CMRR of 50.7dB
(highly resistor matching limited) with 1% tolerance
resistors, and 86.6dB with the LT5400. In this case,
a 2.5V common mode input would result in an offset
of 1.5mV with 1% thick-fi lm resistors and an offset of
23μV with the LT5400, making it suitable for 18-bit ADC
applications where DC accuracy is critical.

Harmonic Distortion

Harmonic distortion is also important when choosing
resistors for a precision application. A large-signal
voltage across a resistor may signifi cantly change the
resistance depending on the size and material. This
p r o b l e m o c c u r s i n a n u m b e r o f c h i p - b a s e d r e s i s t o r s , a n d
naturally becomes more severe as the power levels at
the resistors increase. Table 1 compares the distortion
of thick fi lm, through-hole, and the LT5400 resistors
based on high power drive and similar power drive.
The results suggest that for a given signal, the LT5400
distorts the signal much less than other resistor types.

Stability

Figure 3 shows a model of the distributed capacitance
between resistors in the LT5400. To achieve high preci­sion matching and tracking in the LT5400, many small
SiCr resistors are confi gured in series and parallel.
As a result of the complex interdigitation, the LT5400
resistors can be modeled as a series of infi nitesimal
resistors with parasitic capacitance between adjacent
segments and between individual segments and the ex­posed pad. In contra st, typical sur face mount resistors,
without the tight layout, typically exhibit signifi cantly
less parasitic capacitance.

The ef fect of inter-r esistor capacitance c an be mitigated
when the exposed pad is grounded. However, even
after grounding the exposed pad, this capacitance still

EXPOSED PAD

C´

EXPOSED

C´

C´

EXPOSED

INTER

C´

R´ R´ R´

R´ R´ R´

EXPOSED

C´

C´

EXPOSED

INTER

EXPOSED PAD

C´

EXPOSED

C´

EXPOSED

C´

INTER

ttt

C´

EXPOSED

C´

C´

EXPOSED

R´

R´

INTER

DN502 F03

Figure 3. A Simple Model of the Distributed Capacitance
in a Matched Resistor IC. The Sum of R′ Components
Creates an Equivalent Single Resistor. The Net Effect of
C′

is 1.4pF and the Net Effect of C’

INTER

EXPOSED

is 5.5pF

affec ts circuit stabilit y by forming a parasitic pole on the
order of the total resistance times the total capacitance.

Since overshoot is inver sely proportional to phase mar­gin, minimizing step response overshoot is a good way
to ensure circuit stability. The uncompensated LT5400
confi gura tion exhibits 27% compared to 17% overshoot
from the 0402 confi guration. However, the compensa­tion capacitor necessary to achieve 8% overshoot is
approximately the same in both confi gurations: 18pF
with the LT5400; 15pF with 0402 resistors. With nearly
identical compensation, the two circuits display similar
stability characteristics.

Conclusion

The actual performance of precision amplifi ers and
ADCs is often diffi cult to achieve since data sheet
specifi cations assume ideal components. Carefully
matched resistor networks, such as those supplied
by the LT5400, enable precision matching orders of
magnitude better than discrete components, ensuring
data sheet specifi cations are met for precision ICs.

Table 1. For a Given Power Level, the LT5400 Behaves More Linearly Than Other Resistor Types

SOURCE HD3 –120.00 AT MAX POWER (12V

RESISTOR TYPE POWER RATING HD3 (56mW POWER) HD3 (1/14th RATED POWER)

LT5400 0.8W –117dBc –117dBc
5% Through-Hole 0.25W –100dBc –114dBc
1% Through-Hole 0.25W –115dBc –119dBc

1206 Thick Film 0.25W –104dBc –115dBc
0805 Thick Film 0.125W –93dBc –117dBc
0603 Thick Film 0.1W –89dBc –117dBc
0402 Thick Film 0.068W –72dBc –104dBc

Data Sheet Download

www.linear.com

= 56mW into 1kΩ)

RMS

For applications help,

call 978-656-4700, Ext. 3741

dn502f LT/AP 0512 196K • PRINTED IN THE USA

Linear Technology Corporation

1630 McCarthy Blvd., Milpitas, CA 95035-7417

●

[phone]

FAX: [phone] ● www.linear.com

© LINEAR TECHNOLOGY CORPORATION 2012