Final2


Azad  R. Karee /Al-khwarizmi Engineering Journal ,vol.1, no. 1,PP 19-25  (2005) 
  
 

 

١٩

Abstract: 
A modification to cascaded single-stage distributed amplifier (CSSDA) design by 
using active inductor is proposed. This modification is shown to render the amplifier 
suitable for high gain operation in small on-chip area. Microwave office program 
simulation of the Novel design approach shows that it has performance compatible 
with the conventional distributed amplifiers but with smaller area. The CSSDA is 
suitable for optical and satellite communication systems.  

 

                  
Al-khwarizmi  
Engineering   

Journal       
                      Al-Khwarizmi Engineering Journal, vol.1, no.1,pp 19-25, (2005)        

 
A New Structure for Cascaded Single-Stage Distributed 

Amplifier Using Proposed Active Inductor Loads 
 
 
 
 
 
 
 
 
 
 
 
 
Keyword: Micro electronic, Microwave, Amplifier, Distributed Amplifier. 
 
1 Introduction: 
The conventional distributed amplifier 
(CDA) was proposed in 1948 and 
originally applied to vacuum tubes [1]. 
With the development of monolithic 
microwave integrated circuits (MMIC) 
during 1960’s [2], the DAs have been 
realized by using on-chip transistor 
technologies such as MOSFET’s [3], 
and MESFET’s [4], as well as GaAs 
MESFET [5]. More recently many 
other technologies were introduced to 
the monolithic distributed amplifier 
world[6]. A schematic representation 
of a DA is shown in Figure(1). In this 
structure, the parasitic capacitors of the 
transistors (Cgs and Cds) together with 
the inductors (Lg and Ld) make two 
artificial transmission lines (gate and 
drain lines). As a result, the effect of 
these capacitors will be absorbed into 
Low-pass filter segments of the 
transmission lines then it is possible to 
obtain amplification over much wider 
bandwidth. The drawback of this 
amplifier is limited gain-bandwidth 
due to its optimum number of stages 
[7]. High gain can be achieved by 
cascading several single stage 
distributed   amplifiers.   The      circuit  
 

 
 
 
structure of CSSDA is shown in Figure 
(2). It is essentially a cascade  
connection of single–stage distributed 
amplifiers with the omission of idle 
gate and drain termination for the 
intermediate stages [8]. The amplifier’s 
gate transmission line is formed by the 
lumped inductors LI and the gate 
capacitance Cgs of T1 where as the 
inductors Ld along with the drain 
capacitance Cds of TN serve as the 
drain artificial line. These input and 
output lumped transmission lines 
match the amplifier to the source and 
load impedance  Ro over the entire 
bandwidth.  The available power gain 
expression is given by [9]: 
 

4

2)1(22
o

N
I

N
m RRgG

−

=                           …….(1) 

 
Where gm is the transconductance of 
the active devices. The input and 
output artificial lines possess much 
larger bandwidth compared with that 
of the inter-stage loads, therefore the 
bandwidth of the amplifier is limited 
by the cutoff frequency of internal 
stage (T2 -TN-1). 

Azad  R. Kareem 
Control and Systems Engineering Dept./University of Technology  



Azad  R. Karee /Al-khwarizmi Engineering Journal ,vol.1, no. 1,PP 19-25  (2005) 
  
 

 

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342

)1
1

1
()

1
1

()2
1

2
(

2

)1
1

1
( 1

4
11

2
1

22
2
11

2
mmmmmm

ww NNNNcic −++++−+=
−

−−
−

−
−

−  

It is given by: 
 

 
                                                
                                         
                                                    

                                                    ……….(2) 
 
Where  CRLm II

2/=  , CdsCgsC += , 
and  CRw Ici /1=  is the cutoff 
frequency of the stages if there is no 
inductance in the drain line of the 
amplifier. Equation (2) can be written 
as follow: 

        wc = wci . γ                     ……….(3) 
 

Table (1) lists some values of m and 
their corresponding to various values 

of  γ  for N=4. 
 
 
 
 
 
 
 

Referring to equation (1), it is clear 
that high gain is obtained with large RI. 
Since LI=mRI2 C, large RI mandates 
large LI for given m and C where by 
the size of the on-chip circuit will be 
increased. The goal of this paper is to 
study this problem and to put a 
suggestion for an effective size 

reduction for the on-chip circuit. 
 

2 Implementation of On-chip 
Inductor: 

The main problem associated with the 
design of microwave integrated 
circuits, such as amplifiers, oscillators 
and mixers in which the inductors are 
essential elements is the physical size 
of these elements. Both resistors and 
capacitors are easy to implement. 
Considerable effort has gone into the 
design of the inductor implementation. 
Figure(3) shows the layout for 
different types of spiral inductors. For 
a given shape, an inductor is 
completely specified by the number of 
turns (n), the turn width (w), the turn 

spacing (s), and the turn diameters:    
din and dout , where davg = 0.5(din + 
dout). There are many expressions for 
the inductance value, one of them is 
given by a monomial expression that 
has the following form 

[10] 54321 αααααβ sndwdL avgout=   
……….(4) 

 
Where the coefficients β and αi are 
layout dependent. For a square,            
β = 1.62 * 10-3 , α1 = 1.21 , α2 = - 0.147 
 α3 = 2.4 , α4 = 1.78 , and α5 = - 0.03. It 
is clear that the value of L depends on 

the size of its layout. 
 

3 Proposed   Active   Inductor 
Implementation: 
Figure (4-a) shows a single stage 
distributed amplifier. The introduction 
of a current source transistor ML in the 
load circuit alters its frequency 

dependent impedance, Figure (4-b). 
 

=LZ   =
x

x

i
V

  +R  
LCgw

Rmg

s
21

1

−

+
 )( jwL   

   
 

)( RLgjwRZ mL +≈                     …….(5) 

actL jwLRZ += 
 

where RLgL mact =                         …….(6) 
 

Equation (6) shows that the amount of 
amplification achieved in the 
inductance value is (gmR) which means 
that the effective inductance is (gmR) 
greater than the actually implemented 
one. This allows the use of a large 
value inductance in the circuit but with 
a small on-chip area. Although the new 
structure of the inductance composed 
of two elements instead of one, the 
transistor has a very small area 
compared with the area of the inductor. 

 

4 CSSDA with Active Inductor 
Loads: 

Previous CSSDA’s have used large 
inductances at the drains. Increasing 

Table.1 
m γ Response 
0 

0.9 
0.5 

1 
1.53 
1.34 

No inductive load 
Maximum bandwidth 
Maximally flat 

 
 



Azad  R. Karee /Al-khwarizmi Engineering Journal ,vol.1, no. 1,PP 19-25  (2005) 
  
 

 

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the gain of the amplifier is achieved 
either by increasing the value of RI in 
equation (1), or by increasing the 
number of stages (N). Since m = 
LI/RI2C, then large RI mandates large 
LI for a given m and C. On the other 
hand increasing N with a given value 
of LI means increasing the size of the 
amplifier. These two points yield 
circuits with larger on-chip area. 
However, Figure (5) shows the 
schematic of a CSSDA designed with a 
new type of inductors called “Active 
Inductors” , each one composed of an 
active device (Mi) plus a small 
inductor. Such implementation of 
inductors reduces the overall on-chip 
circuit area without any effect on the 
performance of the amplifier. The 
available power gain can also be 

determined using equation (1). 
A RF signal from a matched generator 
is coupled by the transconductance of 
the active device (Ti) at each stage, and 
finally terminated by the matched 
output load port. At each stage, the RF 
signal will be boosted and terminated 
by the load resistor (RI). The amplified 
signal is valid only up to the cut-off 
frequency, which is controlled by the 

elements values of equation (2). 
To demonstrate the effectiveness of the 
developed methodology, a four stage 
amplifier is designed with gain about 
23dB and bandwidth of 10 GHz. The 
elements values are: RI = 40 Ω , LI = 
0.42 nH , C = 0.6 pf , and gm = 
0.06 1−Ω . The circuit was implemented 
using microwave office program. The 
S-parameters extracted from the 
measurement data are shown in Figure 
(6). The circuit is also implemented 
using active inductors (with LI = 0.1 
nH and gm = 0.15 1−Ω ) and its 
measurement data are shown in Figure 
(7). It is interesting to note that, 
compared to the conventional CSSDA, 
the CSSDA with active inductor loads 
achieve the same results (forward gain 

S21  the reflection losses S11 and S22) 
but with smaller inductance. 

 
5 Conclusion: 
In this paper a new design of cascaded 
single-stage distributed amplifier using 
the novel active inductor loads is 
demonstrated. The new structure has 
unique benefits over the conventional 
CSSDA in terms of high gain and area 
saving. The structure also allows very 
simple design procedure. A four-stage 
amplifier was implemented using the 
developed technique to achieve gain 
≈23 dB and bandwidth ≈ 10 GHz. 
Hence, the CSSDA design is suitable 

for optical and satellite applications. 
 

References:  
E. Ginzton, W. Hewlett, J. Jasberg and 
J. Noe., “Distributed Amplification”, 
Proc. IRE. Vol.36, pp. 956-969, Aug. 

1948. 
1. R. A. Pucel, “Design 

Considerations for Monolithic 
Microwave Circuits”, IEEE Trans. 
Mic. The. Tech., Vol.29, pp. 513-
534, June 1981. 

2. F. Schar, “Distributed Amplifiers 
Using Microstrip ”, Int. J. 
Electronics, Vol.34, pp. 721-730, 
1973. 

3. W. Jutzi, “A MESFET Distributed 
Amplifier with 2 GHz Bandwidth”, 
Proc. IEEE, pp. 1195-1196, June 
1969. 

4. E. W. Strid and K. Gleason, “ A 
DC-12 GHz Monolithic GaAs FET  
Distributed Amplifier ” IEEE 
Trans. Mic. The. Tech., Vol.30, pp. 
969-975, July 1982. 

5. M. Green, S. Lee, K. Chu, J. Webb, 
and F. Eastman, “High Efficiency 
Monolithic Gallium Nitride 
Distributed Amplifier ” , IEEE 
Microwave letters, Vol.10, pp. 270-
272, July 2000. 



Azad  R. Karee /Al-khwarizmi Engineering Journal ,vol.1, no. 1,PP 19-25  (2005) 
  
 

 

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6. T. Wong, “Fundamentals of 
Distributed Amplification”, Artech 
House, 1993. 

7. A. Worapishet, M. 
Chongcheawchamnan, and S. 

Srisathit, “Broadband 
Amplification in CMOS 
Technology using Cascaded 
Single-Stage Distributed 
Amplifier”, 

      Electronics letters, Vol.38, pp. 675-
676, July 2002. 

8. J. Y. Liang and C. S. Aitchison, 
“Gain Performance of Cascade of 
Single-Stage Distributed 
Amplifiers”, Electronics letters, 
Vol.31, pp. 1260-1261, July 1995. 

9. S. Mohan, M. Hershenson, P. 
Boyd, and H. Lee, “Simple 
Accurate Expressions for Planar 
spiral Inductances”, IEEE J. of 
Solid-State circuits, Vol.34, pp. 
1419-1424, Oct. 1999. 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 

 
 
  
  
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
Figure(1) Schematic circuit of N-stages CDA 

 

Figure(2) Schematic circuit of N-stages CSSDA 
 



Azad  R. Karee /Al-khwarizmi Engineering Journal ,vol.1, no. 1,PP 19-25  (2005) 
  
 

 

 ٢٣

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Figure(3) On-chip spiral inductor realizations: (a) square, (b) hexagonal,           
                (c) octagonal, and (d) circular. 

 

 

Figure(4) Single stage of DA.(a)simple common source amplifier.(b)the 
amplifier with active inductor.(c)the equivalent model of the active inductor. 

 
 

 

Vdd 

ML 

(a) (b) (c) 



Azad  R. Karee /Al-khwarizmi Engineering Journal ,vol.1, no. 1,PP 19-25  (2005) 
  
 

 

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 Figure(5) Proposed CSSDA 

Figure(6) Simulated S-parameters in the CSSDA 
with passive inductors (LI= 0.42 nH) 

Figure(7) Simulated S-parameters in the CSSDA 
with active inductors (LI= 0.1 nH) 

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Frequency (GHz)

dis

-20
-15
-10
-5
0
5

10
15
20
25
30
35
40

DB(|S[1,1]|)
cssda

DB(|S[2,1]|)
cssda

DB(|S[2,2]|)
cssda

 

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
F requency (G Hz)

dis

-20

-15
-10

-5

0

5

10

15

20

25

30

35

40
DB(|S[1,1]|)
cssda

DB(|S[2,1]|)
cssda

DB(|S[2,2]|)
cssda

 



Azad  R. Karee /Al-khwarizmi Engineering Journal ,vol.1, no. 1,PP 19-25  (2005) 
  
 

 

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  هيكلة جديدة  للمضخمات التوزيعية باستخدام احمال حثية فعالة
  

  زاد رحيم كريمآ
  لـوجـيةوالجامـعة التكن/ قسم هندسة السيطرة و النظم

  
 :الخالصة

 البحث يتناول دراسة موجزة لمضخمات أشارات الترددات المايكوية ذات النطاق الواسع جدا باستخدام مبدا             
 (Cascaded Single Stage Distributed Amplification) كبير في تطبيقات االتصاالت  لالذي يستخدم بشك

هذا النوع من المضخمات  يضم في تركيبته محاثات في دائرة . البصرية و انظمة االتصاالت عبر االقمار الصناعية
 (integrated circuits)    ةان حجم المحاثة هو احد اهم المشاكل التي ترافق تصميم الدوائر المتكامل. الخرج

من المضخمات بحيث اصبحت تستخدم نوع مستحدث من المحاثات  تقنيةال ههذتم تطويرلذلك , لالنظمة المايكروية
التشكيل .الهدف االساسي منها هو انها تحتاج مساحة اقل عندما تصمم على الدوائر المتكاملة " محاثات فعالة"سميت 

الذي هو مختص باالنظمة المايكروية وكانت نتائج  (Microwave Office)ام برنامج الجديد للمضخم أختبر باستخد
 . التقليدي مع فرق انه يحتاج حجوم اصغر للمحاثات للمضخم الجديد مطابق بكفائته  المضخماالختبار هو ان