Application Report
SNOA506A – September 2007 – Revised May 2013

AN-1719 Noise Figure Analysis Fully Differential Amplifier.....................................................................................................................................................
ABSTRACTThis application note provides noise figure analysis for fully differential amplifiers, including output noisecalculation and noise figure calculation.

1
2
3
4Contents
Introduction .................................................................................................................. 2
Output Noise Calculation for Fully Differential Amplifiers .............................................................. 3
Noise Figure Calculation for Fully Differential Amplifiers .............................................................. 4Conclusion ................................................................................................................... 5
List of Figures1

Simplified Conceptual Diagram of Fully Differential Amplifier ......................................................... 2

2Fully Differential Amplifier Noise Model .................................................................................. 3

3

Noise Analysis Example for Av=1 ........................................................................................ 44

Noise Figure and Voltage Noise Spectral Density vs Gain ............................................................ 5

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Introduction

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Introduction
Fully Differential Feedback Amplifiers (FDA) such as the LMH6550, LMH6551 and the newly released
LMH6552 are used to provide balanced, low distortion amplification and level shifting to wide bandwidth,
differential signals. A simplified conceptual diagram of an FDA is shown in Figure 1 where two forward
paths amplify the two complementary halves of the differential signal. A separate common mode feedback
circuit controlled by the VCM control input sets the output common mode voltage independent of the input
common mode, as well as forcing the ON and OP outputs to be equal in magnitude and opposite in phase.
RF1RG1

IPON-+-+-+-VIN

VOUT = VIN
VOUT+RG2

IN-

RG

Where
VCM+-RF+OP

RF = RF1 = RF2
RG = RG1 = RG2

VCM
RF2Figure 1. Simplified Conceptual Diagram of Fully Differential Amplifier
The LMH6552 FDA is a 1.5 GHz device using TI's proprietary, differential Current Feedback (CFB)
architecture to allow operation at gains greater than unity with exceptional gain flatness, and without
sacrificing bandwidth. With 450 MHz of 0.1 dB unity gain flatness, the device is ideally suited to driving arange of 8- to 14-bit high-speed ADCs, including the Giga Sample 8 bit family and the ADC14DS105, in avariety of wideband Nyquist applications.
In designing an FDA to drive an ADC it is required to ensure that the FDA does not degrade the ADC’s
signal to noise and distortion (SINAD) performance. A key element of this analysis is determining andoptimizing the noise performance of the FDA. The remainder of this article will show how the FDA output
noise spectral density and noise figure can be calculated for factoring into the overall system noiseanalysis. Voltage Feedback (VFB) FDAs have historically been constrained to operating at low gain due totheir poor noise performance at higher gains. This article will show that the LMH6552 CFB architecture
overcomes this constraint, delivering a noise advantage as well as a gain bandwidth advantage overalternative VFB devices.

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Output Noise Calculation for Fully Differential Amplifiers

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RF1
VRS

Rs

RG1

VRF1

VRG1
VN

VRS

INP
VNO

RT
RG2

VRG2
INM

RF2

VRF2

Figure 2. Fully Differential Amplifier Noise Model2

Output Noise Calculation for Fully Differential Amplifiers
The noise model for a general purpose FDA is shown in Figure 2. INP and INM are the input referred noisecurrents for the FDA’s positive and negative input terminals respectively, and VN is its input referred noisevoltage. Included in the model are noise sources associated with resistive elements in the feedback andsource termination networks.
The total output referred noise density VNO in nV/√Hz, is calculated by taking the root square sum (rss) of
the output referred noise from each source in the model. Since we are primarily interested in how noiseinternal to the FDA influences overall system noise performance, we separate the equation for VNO into
two components; the first being due to the input referred noise from the FDA, VNOFDA, and the second dueto thermal noise from the resistive feedback network, VNOFB.
VNO =2V NO

FDA+ V NOFB

2(1)

In most differential signaling applications CMRR and balance error are key. The differential feedback
network is balanced by selecting RF1=RF2=RF and RG1=RG2=RG, so both positive and negative feedback
factors are matched and symmetric. Replacing RS and RT with their Thevenin equivalent source
resistance, RSTH=RS||RT, the FDA and feedback network output noise densities are:2

§ RF + R GEQ·2222=V¨ R¸ + INP RF + INM RFNFDA© GEQ ¹
2V NO

22V NOFBRG

EQ2(2)§ RF ·§ RF ·¸ + 4kTRs(RSSTH) ¨R ¸RG© EQ ¹© GEQ ¹2= 4kT(2RF) + 4kT(2RG) ¨= RG +RS || RT2(3)The impact of external resistor noise is determined by the differential feedback topology ( Equation 2),
regardless of whether a CFB or VFB FDA is chosen. However, the influence of the FDA on total output
noise density Equation 1) can largely be influenced by the choice of FDA architecture.
In a VFB FDA, the differential input impedance is very high (usually hundreds of KΩ to several MΩ), andnoise sources internal to the FDA will tend to refer to the input as voltages. Consequently, input referrednoise currents will be quite small, on the order of a few pA/√Hz, and will only contribute a significant
portion of the total output noise when RF is large, which is usually not the case. Note that the gain term for
VN in Equation 1 is simply the reciprocal of the equivalent feedback factor βEQ which is related to thedifferential amplifier’s closed loop gain G by:

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Noise Figure Calculation for Fully Differential Amplifiers
RF

G=RG

=

EQ

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1- 1.
EEQ

(4)

Neglecting INP and INM, Equation 1 can be re-written as:
V NO

2

FDA

2

# VN (G + 1)2(5)In other words, operating a VFB FDA at high values of gain is necessarily accompanied by a proportional
increase in output noise density, and can lead to degradation of overall noise performance when the FDA
is a significant source of noise in a system.
A very different result arises when a CFB FDA, such as the LMH6552, is considered. Here, the differential
input stage is essentially a current controlled current source, with ideally zero differential input impedance.
As a consequence noise sources internal to the amplifier tend to refer to the inputs as currents, rather
than as voltages, and the total FDA output noise will be dominated by the sum of input noise currents INPand INM multiplied by the feedback resistor squared.
V NOFDA2§©

·¹# ¨INP + INM ¸ RF222(6)Unlike a VFB FDA, the output noise of a CFB FDA depends on the value of RF rather than on theamplifier’s gain. Hence, increasing the gain by reducing RG does not appreciably degrade the noise
performance of the circuit. This is an extremely important result and highlights one of the key advantagesof using a CFB FDA over a VFB FDA in differential signaling applications.

3

Noise Figure Calculation for Fully Differential Amplifiers
In many high-speed systems, noise performance is often described in terms of the system noise figure,which is 10 log of the signal-to-noise ratio at the system’s input divided by the signal to noise ratio at itsoutput. Noise figure is a quantitative measure of how much noise is added to a given signal as itpropagates through a processing chain, and for amplifiers can be conveniently expressed as the ratio ofoutput noise density to source noise density by the following equation.
V NO§·NF = 10 log ¨¸;
2D 24kTRsG
T©
¹2RTDT =RS + RT(7)The product GDT is the voltage gain of the amplifier from VS to VO including the signal attenuation of theinput termination network.
301

100

VS

301

200

121
301

301

Figure 3. Noise Analysis Example for Av=1

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Conclusion

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3030LMH6550 (VFB)20

NF (dB)NF
2015VNO

1510105LMH6552 (CFB)
5-8 -6VNO (nV/rtHz)

25250-4-20246810 12GAIN (dB)Figure 4. Noise Figure and Voltage Noise Spectral Density vs Gain
To highlight the difference in noise performance between CFB and VFB FDAs, the application circuit ofFigure 3 is used to calculate the output noise spectral density and noise figure at various values of gainusing both the LMH6552 (CFB) and LMH6550 (VFB) FDAs in a 100Ω system. RF is held at 301Ω and thetermination resistor RT is adjusted at each value of gain to maintain a 100Ω differentially terminated input.
The results are presented graphically in Figure 4.
At low gain, the two parts offer similar noise performance, with the LMH6552 having a roughly 2 dB edge
in noise figure at a gain of -6 dB. However, as gain is increased, the CFB FDA's noise figure improves at a
substantially higher rate, giving a 6.5 dB improvement at a gain of 9.5 dB.

4Conclusion
The choice between a current or voltage mode FDA may depend on many factors and will ultimately comedown to which amplifier works better within a given system specification. Where low-noise, widebandwidth applications require the FDA to be configured for larger than unity gain CFB FDAs can offer anelegant solution.

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