Computer Program Calculation for Distortion of Wide-Band Track and Hold Amplifier

doi:10.4236/jcc.2013.16001

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Journal of Computer and Communications, 2013, 1, 1-4

Published Online November 2013 (http://www.scirp.org/journal/jcc)

http://dx.doi.org/10.4236/jcc.2013.16001

Open Access JCC

Comput er Pr o gr a m C alcu lation for Di s t or ti on of

Wide-Band Track and Hold Amplifier

Hailang Liang1,2, Jin He1,2, Xiaoan Zhu2,3, Xiaomeng He2, Cheng Wang2,3, Lin He2, Gui Liu2,

Qingxing He4, Caixia Du4

1Tera-Scale Research Center, Institute of Microelectronics, School of Electronic Engineering and Computer Science, Peking Univer-

sity, Beijing 100871, China; 2Peking University Shenzhen SOC Key Laboratory, PKU-HKUST Shenzhen-Hong Kong Institution,

Shenzhen 518057, China; 3Dong Guan Xin Cheng Electronic Technology Ltd. Co., High-Tech Industrial Development Zone, Song-

shanhu Lake, Dongguan, China; 4Shenzhen Huayue Terascale Chip Ltd. Co., Shenzhen 518045, China

Email: [email protected]

Received June 2013

ABSTRACT

Tow different computer calculation methods for distortion of the wid e-band diode bridge track and hold amplifier (THA)

are presented based on a high frequency Schottky diode model. One of the computer programs calculates the distortion

of weekly nonlinear THA based on the KCL and the nonlinear-current method. The other calculates the weekly nonlin-

ear distortion by using a Volterra series method and a nodal formulation. Comparative calculation results for the diode

bridge THA have shown good agreement with these two computer program calculation methods, whereas the overall

computational efficiency of the nonlinear-current method is better than that of the nodal formulation method in a special

evaluation.

Keywords: Track and Hold Amplifier; Broadband Amplifiers; High-Speed Integrated Circuits; Schottky Diode

Frequency Converters; Harmonic Distortion; Volterra Analysis; Compute r Pro gram; Nonlinear-Current

Method

1. Introduction

A diode bridge architecture THA prior to the analog to

digital converters are used to implement low-cost ultra

high speed transceivers. Distortion is one of the impor-

tant factors that limit the dynamic range of THA [1]. It is

crucial to predict and calculate the distortion in the

weakly nonlinear circuit by computer program cal-

culation or simulation. Several methods used to resolve

the distortion issues are shown in [2-6]. Two computer

programs based on these methods are implemented to

evaluate the distortion of THA with an improved proce-

dure in terms of the Volterra series.

In this paper, two computer program are used to cal-

culate the weakly nonlin ear distortion of the diode bridge

switch THA based on the high frequency Schottky diode

model in terms of a Volterra-series analysis. Section 2

describes a diode bridge THA for ultra high speed appli-

cation. In Section 3, the high speed diode model,

assumptions and distortion analysis are presented. The

computer program description is proposed in Section 4.

Section 5 shows the program calculation results and then

follows by concl usion.

2. A Diode Bridge THA

Consider a diode bridge THA shown in Figure 1, which

is directly derived from Fig ure 2 in [7], this circuit con-

sists of a high-speed Schottky diode bridge (

to 4

used as a switch between the input and output, a hold

Figure 1. A diode bridge track and hold amplifier [ 7].

Computer Program Calculation for Distortion of Wide-Band Track and Hold Amplifier

Open Access JCC

Figure 2. Program flow chart for calculating the distortion

[4,10].

capacitor

to maintain the sampling voltage, a diffe-

rential pair (

and

) to turn on/off the diode bridge

switch, two load inductors used to extend bandwidth, two

load resistors, a bootstrap buffer, a output buffer and a

current tail. This THA with diode bridge configuration is

suitable for wideband and high speed application [7].

3. Model, Assumptions and Distortion

Analysis

As shown in [8]. A simplified equivalent circuit for the

diode bridge THA in track mode is illustrated in Figure

3(a).

The first order Volterra kernel

)(

is given by

the following Equation (1) [1].

=)(

ωω

(1)

The second order and the third Volterra kernel

),(

212

ωω

jjH

and

),,(

3213

ωωω

jjjH

are shown in

Equation (2) and Equation (3) respectively. Equation (2)

and Equation (3) imply that if

1=)(

, the Vol-

terra kernels

),(

212

ωω

jjH

and

),,(

3213

ωωω

jjjH

tend to zero.

)(

))((1

=),(

212

ωω

jjC

jjH

+++−

−−

(2)

21211

31 23

123

11111 1

123

(,)(() 1)

( ,,)=1()

(13()3() ())

61()

IHj jHj

Hj jjICj

IHjH jHj

VICj

ωω ω

ωωω

ω ωω

ωωω

−

−−+ +

+− +−

−−+ +

(3)

The third-order harmonic distortion HD3 is the ratio of

the amplitude of the third-order harmonic to the ampli-

tude of the fundamental harmonic. With the Volterra co-

efficients,

is defined as followings [1,9].

(a) (b)

Figure 3. A simplified equi val ent c irc uit for the di ode br idge

THA.

Computer Program Calculation for Distortion of Wide-Band Track and Hold Amplifier

Open Access JCC

3213

|)(|

|),,(|

jjjH

HD 

ωωω

(4)

The third-order intermodulation distortion which is the

ratio of third-order kernel to the first-order kernel can be

expressed as [1].

3213

|)(|

|),,(|

IM 

ωωω

(5)

In term of Volterra analysis, one can choose the appro-

priate values for the bias current and the hold capacitor,

, to yield a suitable

performance [1].

4. Computer Progr am D es crip tio n

(1) Nonlinear-current method:

The KCL and the nonlinear-current method are used in

this program. The detailed description of the nonlinear-

current method was proposed in [5,6], [4] and [10]. In

this approach the small-signal I/V characteristic for a

simple voltage-controlled conductance is expressed as

[10]:

...=

+++++ vgvgvgvgvgi

(6)

where the first-order voltage

)(tv

)(

=)(

tjexpvtv

qqs

∑

−

(7)

the second-order curre nt [4 ,10] is

221

21, 1,

121 2

()= ()

[ ()]

qqq q

q QqQ

i tgvt

gvvexp jt

ωω

−−

∑∑

(8)

This program is implemented in Python in terms of the

nonlinear-current method and KCL [4,10]. The linear

resistors, diodes, capacitors, inductors, controlled sources,

transmission lines and the nonlinear resistors, diodes,

capacitors, and controlled sources are used in this pro-

gram for calculating the distortio n of Volterra series. The

flow chart for the program is illustrated in Fig ure 2,

where the basic algorithm used in this paper is depicted

in [4,10].

The program first initializes the environmental vari-

ables, which includes setting up the values of the re-

sistors, the capacitors, the diodes, the inductors, the

VCCS etc. and replacing every non-linearity with its

linearized equivalence.

Then the program begins to calculate the first order

voltage with linearized equivalence [4]. The output data

are saved and then the second and the third order currents

and voltages are computed, the calculation of these

higher order currents and voltage depends on those of the

lower order ones that have been saved. As shown in the

flow chart, the related currents and voltages are solved

for each order and the desired corresponding responses

are derived from the Volterra series.

(2) Volte r r a series and nodal formulation method:

The flow chart of this method is shown in Figure 4.

More detailed description of this method is depicted in

[11]. To compare with the results from those of non-

linear-current method, the program has been rewritten in

Python languag e .

5. Calculation Results

Figure 5 illustrates the IIP3 versus input frequency re-

sults of both nonlinear-current method and nodal for-

mulation method, which indicates that these two results

have a good agreement in the range of the input fre-

quency.

The results of the HD3 versus input frequency for both

nonlinear-current method and nodal formulation method

Figure 4. Program flow chart for the computation of vol-

terra kernels [2].

Computer Program Calculation for Distortion of Wide-Band Track and Hold Amplifier

Open Access JCC

Figure 5. Comparison of third-order inter cept point.

Figure 6. HD3 characteristics of diode bridge THA.

are illustrated in Figure 6, it shows that they are also

similar and have the agreement between them.

At some special test condition, the calculation time

results of both nonlinear-current method and nodal for-

mulation method are illustrated in Table 1. Obviously,

the calculation times of the nonlinear-current method is

much less than those of nodal formulation method with

the specified input frequency.

6. Conclusion

Nonlinear-current method and nodal formulation method

for distortion calculation of the diode bridge configura-

tion THA are presented by using a simplified high-speed

diode model. Comparative results show that the cal-

culation results derived by the nonlinear-current method

is consistent with thos e of the nodal formulation method,

whereas the overall calculation time of the nonlinear-

current method has been improved.

7. Acknowledgements

This work is supported by the Industry Education and

Table 1. Summary of calculation time.

Frequency (GHz) 1 3 5

Nonlinear-current method (Sec) 12.78 36.42 42.75

Nodal formulation method (Sec) 25.17 72.49 87.73

Research Foundation of PKU-HKUST Shenzhen-Hong-

kong Institution (sgxcyhzjj201204), by the Guangdong

Natural Science Foundation (S2011040001822) and the

Fundamental Research Project of Shenzhen Science and

Technology Foundation JCYC20120618163025041 . This

work is also supported by the National natural Science

Funds of China (61204033, 61204043).

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