LMH3401 Datasheet, PDF (24/48 Pages) Texas Instruments – LMH3401 7-GHz, Ultra-Wideband, Fixed-Gain, Fully-Differential Amplifier

LMH3401
SBOS695A – AUGUST 2014 – REVISED DECEMBER 2014
www.ti.com
Feature Description (continued)
Solving this quadratic for R_T starts the solution sequence, as shown in Equation 2:
R
2
T
R
T
2R_F
2R_S
§
¨©
2R
F

R_S
2
A
2
V
·
¸¹
2  A _V   R _S A _V (4 
A _V)

2R_F
2

2R
F^R
2
S
A
V
A_V  R_SA_V
(4

A _V)
0
(2)
Being a quadratic, there are limits to the range of solutions. Specifically, after R_F and R_S are chosen, there is
physically a maximum gain beyond which Equation 2 starts to solve for negative R_T values (if input matching is a
requirement). With R_F selected, use Equation 3 to verify that the maximum gain is greater than the desired gain.
ª
«
4 ^RF
º
»
Av _max
^RF
R_S

2 ‡
««_{1 }
«
1
R_S
( ^{R F}  2)²
»
»
»
«¬
R_S
»¼
(3)
If the achievable A_Vmax is less than desired, increase the R_F value. After R_T is derived from Equation 2, the R_G1
element is given by Equation 4:
R_G1
2 ^RF
A_V
 R_S
1 ^RS
R_T
(4)
Then, the simplest approach is to use a single R_G2 = R_T || R_S + R_G1 on the non-signal input side. Often, this
approach is shown as the separate R_G1 and R_S elements. This approach can provide a better divider match on
the two feedback paths, but a single R_G2 is often acceptable. A direct solution for R_G2 is given as Equation 5:
2 ^RF
R_G2
A_V
1 ^RS
R_T
(5)
This design proceeds from a target input impedance matched to R_S, signal gain A_V, and a selected R_F value. The
nominal R_F value chosen for the LMH3401 characterization is 200 Ω. As discussed previously, this resistance is
on-chip and cannot be changed.
Note that when driving the LMH3401 with a 50-Ω source impedance the on-chip resistor is R_G1 and the other
input requires only 50 Ω to complete R_G2. The above equations are provided to help show the effects of the
active termination and to assist when using the LMH3401 with source impedances other than 50 Ω.
9.3.2.2 Input Impedance Calculations
The designs so far have included a source impedance, R_S, that must be matched by R_T and R_G1. The total
impedance with respect to the input at R_G1 for the circuit of Figure 54 is the parallel combination of R_T to ground
and ZA (active impedance) presented by the amplifier input at R_G1. That expression, assuming R_G2 is set to
obtain a differential divider balance, is given by Equation 6:
§
¨¹

R
G1
·
¸
§
¨¹

R_F
·
¸
ZA R_G1 ^©
R _{G2 ¹ ©} R _{G1 ¹}
2  ^RF
R _G2
(6)
For designs that do not need impedance matching (but instead come from the low-impedance output of another
amplifier, for instance), R_G1 = R_G2 is the single-to-differential design used without R_T to ground. Setting R_G1 = R_G2
= R_G in Equation 6 gives the input impedance of a simple input FDA driving from a low-impedance, single-ended
source to a differential output.
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