127

CHAPTER 6

VECTOR MODULATORS

6.1 INTRODUCTION

Beamforming systems use phased array antennas. Beamforming

performs spatial filtering of the radiation lobes of the array of antennas by

directing the radiation lobes towards the desired direction with appropriate

analog or digital processing techniques as proposed by Frank Gross (2005). A

narrow band phased array designated to yield single antenna beam can be

obtained with phase shifters or vector modulators. Vector modulators are used

in adaptive beamforming systems to change the phase of the signal. It

improves the directivity of RF waves in Wireless systems. Vector modulator

is compact, consumes low power and modulates the signal with moderate

loss. Vector modulator allows the reduction of the side lobe level, while being

able to accurately point the antenna beam in any direction (John Penn 2005).

Vector modulators are used to change the phase of the signal in azimuth

direction as proposed by Fakoukakis et al (2005). Phase shifts ranging

between 0o

to 3600

can be obtained in the azimuth direction by varying the

control signal given to the vector modulator.

The requirements for vector modulators are Phase/Amplitude

accuracy over the system bandwidth, the range of phase shifts, minimum

amplitude variations between the phase states, minimal insertion loss and low

power consumption. Among the above requirements minimum insertion loss

is of key importance, because it affects the system noise figure. The vector

128

modulator must be tunable for different phases of the signal. If the same

vector modulator is used on both transmit and receive paths, then it is said to

be reciprocal.

Vector modulator being an analog circuit, offers unlimited

resolution capability. Any sinusoidal signal can be expressed as a vector

having the properties of both amplitude and phase with respect to a reference

signal. If a signal is represented as a vector in a polar coordinate system with

coordinates of amplitude and phase, it can also be defined in a rectangular

coordinate system as In-phase (I) and Quadrature (Q) components of the

output signal.

In this chapter, the vector modulators with active devices as control

elements are proposed for three different frequencies. The transmitter operates

in the frequency band of 935-960MHz and receiver operates in 890-915MHz

in the 900MHz band transceiver at the base station. 900MHz system operates

with a bandwidth of 25MHz. Vector modulator for transmit and receive path

are designed separately for the beamforming system operating in 900MHz

band. Since both transmitter and receiver operate in the same frequency band

of 2390-2410MHz with 20MHz bandwidth. Reciprocal vector modulator is

designed for the beamforming system operating in 2.4GHz band. The

specifications of the vector modulators are given in the Table 6.1.

Table 6.1 Specifications for Vector Modulator design

Frequency band

(MHz)

Center frequency

(MHz)

Transmitter End 935-960 947.5

Receiver End 890-915 902.5

Transmitter and

Receiver2390-2410 2400

129

The vector modulators are implemented using variable attenuators.

Output of the vector modulators is analyzed at the transmitter and receiver

end for wireless systems operating at 900MHz and at 2.4GHz.

6.2 LITERATURE SURVEY

Several literature give the design and implementation of vector

modulators. Wenjiang Wang et al (2008) has proposed vector modulator with

digital variable attenuators and phase shifters. The digital attenuators are easy

to be implemented in IF frequency range. For passive and active beamforming

at RF range digital attenuators are not preferred. Hence Vector modulators

with analog components are preferred. Passive components alone can be used

to realize vector modulators, but to have control on the phase shift active

devices like JFET and MOSFET are used. Vector modulator using MESFET

and microstrip lines for beamforming network is proposed by Jesus Grajal et

al (1997). Frank Ellinger et al (2000) has proposed vector modulator with

GaAs MESFET device for 4.8-5.8GHz for smart antenna receivers. Vector

modulator with single control voltage has been proposed Frank Ellinger and

Werner Batchtold (2002). Vector modulator for Ka-band using MESFET is

proposed by John Penn (2005). Basic building blocks of vector modulator are

Hybrid coupler, Variable Attenuator (VA) and Wilkinson combiner. Fardin et

al (1996) has proposed hybrid coupler design using lumped elements. Hybrid

coupler design is based on the principles proposed by Robert Frye et al

(2003). Design of Variable Attenuator is proposed by John Penn (2005).

Liang-Hung Lu et al (2005) has proposed Wilkinson power dividers for

4.8GHz center frequency. The Wilkinson power combiner is implemented

based on the operation of power dividers proposed by Wilkinson (1960) and

power combiners proposed by Andreas Wentzel et al (2006).

130

6.3 PROPOSED VECTOR MODULATORS

Vector modulator performs phase shift of the signal in azimuth

direction with added benefit of amplitude control. Azimuth direction of the

signal is represented by the . The principle of the phase change by means of

a vector modulator originates from the vector diagram. If two signals

represented by vectors as in Figure 6.1 have a phase difference between

them, by changing the magnitude of these signals by means of Variable

Attenuators the amplitude and the phase ( ) of their vector sum changes.

Figure 6.1 Phase shifting vector diagram

The magnitude of the resultant vector is given by

2 2

1 2 1 2G3 G G 2G G cos( ) (6.1)

where G1 and G2 are the control coefficients of VGAs or VAs. The phase,

of the resultant vector is given by

1 2

1 2

G sin( )tan

G G cos( ) (6.2)

G1

G2

G3

131

The general block diagram of a vector modulator is shown in

Figure 6.2.

Variable

Attenuator

Wilkinson

Splitter

Variable

Attenuator

90o Hybrid

I I

Q QPhase and

Amplitude

modulated

signal

Input Signal

Figure 6.2 Vector Modulator Block Diagram

The vector modulator is built using hybrid coupler, Wilkinson

combiner and two variable attenuators. Hybrid coupler is a four-port

directional coupler that is designed for a 3dB (equal) power split. The

Wilkinson combiner is a power combiner. The input signal is divided into two

equal signals which are 90° apart, i.e., I & Q signals. I and Q components of

the signal are then passed through independent variable attenuators, which

can also provide 180° phase shift. Magnitude of I and Q signals are varied

using VAs. This allows the magnitude of each signal to be re-located along its

vector axis. The two signals are then combined using Wilkinson combiner.

Sum of these input vectors produces the resultant output signal. The required

phase shift at the center frequency is obtained by the control voltage of the

variable attenuator. I & Q control of vector modulator allows the reduction of

the side lobe level and accurately point the antenna beam in any direction.

132

1

4 3

2INPUTOUTPUT

-3dB

ISOLATEDOUTPUT

-3dB

3 dB

Quad Hybrid

Coupler=90o

6.3.1 Hybrid Couplers

Hybrids couplers are of two types, 90° or quadrature hybrids and

180° hybrids. In this proposed vector modulator circuit, 90° degree hybrid

couplers are considered. The basic configuration of a 90° hybrid coupler

shown in Figure 6.3 illustrates two cross-over transmission lines over a length

of quarter wavelength, corresponding to the center frequency of operation.

Figure 6.3 90° Hybrid Coupler

When power is introduced at the input port, half the power (3dB)

flows to the port 2 and the other half is coupled to the port 3. Reflections from

mismatches sent back to the output ports will flow directly to the port 4 or get

cancelled at the input. This makes hybrids more suitable to split high power

signals in applications where unwanted reflections could easily damage the

driver device. 3dB, 90° hybrids are also known as quadrature hybrids because

a signal applied to any input, will result in two equal amplitude signals that

are 90° out of phase. The relationship at the output remains the same as these

devices are electrically and mechanically symmetrical. This configuration

ensures a high degree of isolation between the two output ports and the two

input ports. The scattering matrix is given in terms of attenuation constant ( )

and phase constant ( ). The scattering matrix for a matched, lossless,

reciprocal 4-port device is given as

133

0 0 j

0 j 0[S]

0 j 0

j 0 0

(6.3)

and for hybrid coupler since 12

, the scattering matrix of quadrature

hybrid coupler is

0 1 0 j

1 0 j 01[S]

0 j 0 12

j 0 1 0

(6.4)

Hybrid coupler implemented using inductive coupling is proposed

by Robert Frye et al (2003). The circuit of Hybrid coupler is shown in

Figure 6.4.

1

3

2

4

CoCo

Co Co

L

L

C1C1

Figure 6.4 Circuit of Hybrid coupler

Hybrid coupler is designed for the desired center frequency using

the following equations for transmitter and receiver by assuming R=50 ohm,

Zo=50 ohm (characteristic impedance)

134

1o

1CZ

(6.5)

1 o

RL( C Z )

(6.6)

20 11C C

L (6.7)

and =2 f, where f is the center frequency. The values of the components

used to simulate the hybrid coupler are given in Table 6.2.

Table 6.2 Designed values of components for Hybrid coupler

Components 902.5MHz 947.5MHz 2.4GHz

L 6.23nH 5.9389nH 2.344nH

C0 3.528pF 1.392pF 0.5498pF

C1 1.468pF 3.359pF 1.3263pF

6.3.2 Wilkinson Power Combiner

The Wilkinson power combiner combines two equal-phase signals

into one signal at the output. Quarter-wave transformers are used to match the

split ports to the common port. Because a lossless reciprocal three-port

network cannot have all ports simultaneously matched, one resistor is added

in between. Wilkinson combiner in its simplest form is an equal-amplitude,

two-way combiner as a three-port circuit is shown in Figure 6.5. The arms are

quarter-wave (4

) transformers of impedance o2Z .

The resistor allows all three ports to be matched; it fully isolates

port 1 from port 2 at the center frequency. The resistor adds no resistive loss

to the power split, so an ideal Wilkinson combiner is 100% efficient. The

135

scattering parameters for the 2-way Wilkinson Power combiner at the design

frequency are given by Pozar (2005) as

0 1 1j

[S] 1 0 02

1 0 0

(6.8)

2Zo

Port 2

Port 3

Port 1

Zo

Zo

1.414Zo

1.414Zo

Zo

Figure 6.5 Circuit of Ideal Wilkinson power combiner

Inspection of the S Matrix reveals that the network is reciprocal (Sij

= Sji), the terminals are matched (S11=S22=S33=0), the output terminals are

isolated (S23=S32=0) and equal power division is achieved (S21=S31). The non-

unitary matrix shows that the network is lossy. No loss occurs when the

signals at ports 1 and 2 are in phase. Circuit of the implemented Wilkinson

combiner is given in Figure 6.6.

For designing the Wilkinson combiner characteristic impedance is

considered to be Z0=50 Ohms. The design equations given by Pozar (2005)

are used to design the Wilkinson combiner with R = 2Z0,

136

p1C

2 R (6.9)

SRL

f 2 (6.10)

and =2 f, where f is the center frequency. The values of the components

used to simulate the Wilkinson combiner are given in Table 6.3.

2Zo

2Cp

Port 1

Port 2

Port 3

CpCp

LS

LS

Figure 6.6 Implemented Wilkinson combiner circuit

Table 6.3 Designed values of components for Wilkinson Combiner

Components 902.5MHz 947.5MHz 2.4GHz

LS 12.46nH 11.87nH 4.6884nH

CP 2.49pF 2.37pF 0.9379pF

137

6.3.3 Attenuators

Attenuators reduce the output signal with respect to the input and

measure the power reduction in decibels (dB). Attenuators are used in

applications that require signal level control. In many RF systems attenuators

are required for automatic gain control of receiver and transmitter systems.

Attenuators are also used for amplitude weighting in phased array systems

and for temperature compensation of RF amplifiers. The degree of attenuation

is controlled by an input signal. Attenuation may be performed on the

received signal to cancel the distortion products gained during transmission.

A RF attenuator may be implemented as a fixed attenuator or a variable

attenuator.

Fixed RF attenuators are used to reduce power levels of a signal by

a fixed amount with little or no reflections. The output signal is attenuated

relative to the input signal while the input and output impedance is maintained

close to 50 ohms over the specified bandwidth. This device is often used to

improve interstage matching in a circuit. Frequency ranges can be in excess of

30GHZ, and attenuation factors are typically in 1, 3, 6, and 10dB steps. Fixed

attenuators can be connected in series to provide with the desired attenuation.

Most of the fixed RF attenuators are designed to handle only small amounts

of RF power and are extremely susceptible to damage because of overloading.

In variable attenuators described by Ng et al (2003), the four FETs

are used for single attenuator. In the proposed variable attenuator two active

devices JFET or MOSFET is used along with hybrid coupler. By controlling

the voltage across the FET or the MOSFET, their RF resistances can be

varied. When designing or using variable RF attenuators, it is necessary to

ensure that the RF attenuator retains constant impedance over its operating

range to ensure the correct operation of the interfacing circuitry. Variable

attenuator has been implemented for controlling the amplitude of the signal

138

using a control voltage. A hybrid coupler is placed along with the variable

attenuator to bring about necessary phase change. The arrangement of

variable attenuator using JFET is shown in Figure 6.7 and variable attenuator

using MOSFET is shown in Figure 6.8.

Co

Co Co

Co

L L

C1

C1

R R

M1M2

control

voltage

Variable attenuator

hybrid coupler

Figure 6.7 Variable Attenuator using JFET and hybrid coupler

Co

Co Co

Co

L L

C1

C1

R R

M1 M2

control

voltage

Variable attenuator

hybrid coupler

Figure 6.8 Variable Attenuator using MOSFET and hybrid coupler

139

Performance metrics for RF attenuators include frequency range,

maximum attenuation, insertion loss, input voltage standing wave ratio, return

loss, and reflected power. Important characteristics of RF attenuator are

accuracy, low Standing Wave Ratio (SWR), flat frequency response.

6.3.4 Vector modulators using JFET and MOSFET

Vector modulators are implemented by using either JFET or

MOSFET as a voltage control device in the variable attenuator of the vector

modulator. The circuit of vector modulator is shown in Figure 6.9.

Hybrid

Coupler

Wilkinson

combiner

Hybrid

Coupler

Hybrid

Coupler

Variable

Attenuator

Variable

Attenuator

control

voltage

control

voltage

input

signal

output

signal

Figure 6.9 Implemented Circuit of Vector modulator

6.4 SIMULATION RESULTS

S-parameter simulation is performed for the Hybrid couplers to find

whether the input signal power is equally split and given to ports 2 and 3

(power at the -3dB point). The S-parameter results are shown in Figure 6.10.

140

a) Return Loss (S11)

b) Isolation (S41)

c) S31 and S21

Figure 6.10 S-parameter results of Hybrid coupler at 902.5MHz

141

d) Phase plot of hybrid coupler

Figure 6.10 (Continued)

From the magnitude plots of Figure 6.10 (a) and (b), it is inferred

that return loss (S11) and isolation (S41) is minimum. Figure 6.10 (c) shows

that at port 2 (S21) and port 3 (S31) equal power split is obtained at half power

point. From the phase plot in Figure 6.10(d), it is inferred that signal at port 2

(S21) and port 3 (S31) are 900 out of phase. The signal at port 1 is split into In-

phase and Quadrature components with equal magnitude by the hybrid

coupler. Values of the S-parameters for the hybrid couplers operating at

different center frequencies of 902.5MHz, 947.5MHz and 2.4GHz are given

in Table 6.4.

Table 6.4 S-parameters of Hybrid coupler

Center frequencyParameters

902.5MHz 947.5MHz 2.4GHz

S21(dB) -3.006 -3.009 -3.008

S31(dB) -3.015 -3.011 -3.012

Phase of S21 (degrees) -90.068 -90.002 -89.999

Phase of S31 (degrees) -0.068 -0.002 0.001

S11(dB) -61.194 -86.157 -72.339

S41(dB) -61.195 -86.159 -72.343

142

The return loss (S11) is 22dB and isolation (S41) is 27dB for the

hybrid coupler proposed by Robert Frye et al (2003). From Table 6.4, it is

inferred that the proposed hybrid couplers provides high isolation and good

return loss for all the three center frequencies.

The simulation responses of the Wilkinson combiner circuit for

902.5MHz are given in Figure 6.11 and the results of Wilkinson combiner for

902.5MHz, 947.5MHz and 2.4GHz are given in Table 6.5.

a) Magnitude of S21

b) Magnitude of S31

Figure 6.11 S-parameters of Wilkinson Combiner

143

c) Magnitude of S11

d) Phase of S21

e) Phase of S31

Figure 6.11 (Continued)

144

Table 6.5 S-parameters for the Wilkinson combiner

S-parameter

dB

Phase of S21 and S31

degreesCenter

frequencyS21 S31 S11 S21 S31

902.5MHz -3.010 -3.010 -58.836 -89.856 -89.856

947.5MHz -3.010 -3.010 -58.288 -89.821 -89.821

2.4GHz -3.023 -3.010 -75.800 -89.995 -89.995

The magnitude of S21 and S31 in Figure 6.11 (a) and (b) shows that

the power is equal at both the ports 2 and 3 at half power point. The

magnitude of S11 in Figure 6.11(c) shows that the reflection loss is low. From

Figures 6.11 (d) and (e), it is clear that the signals at port 2 and port 3 are in

phase. The magnitude of the power is high at port 2 and port 3 at the designed

frequencies for the Wilkinson combiner and the return loss is very low. The

phase of S21 and S31 shows that the signals are in phase. This circuit

effectively combines the input signals at port 2 and port 3 into a single signal

with minimum loss.

The circuit simulation results of the variable attenuator are given in

Figure 6.12. The attenuation produced by the variable attenuator for

902.5MHz, 947.5MHz and 2.4GHz with JFET and MOSFET as active

devices are given in Table 6.6.

Table 6.6 Attenuation produced by variable attenuator with JFET

and MOSFET

JFET MOSFET

Center

frequency

Input

signal

magnitude

dB

Output signal

magnitude

dB

Input

signal

magnitude

dB

Output signal

magnitude

dB

902.5MHz 0 -20.407 0 -12.162

947.5MHz 0 -20.433 0 -11.595

2.4GHz 0 -15.087 0 -11.337

145

(a) Input to the attenuator

(b) Output of the Attenuator

Figure 6.12 Simulation Results of Variable Attenuator

146

The variable attenuator uses single control voltage for the

operation. The variable attenuator is simulated for three different frequencies

of 902.5MHz, 947.5MHz and 2.4GHz. The variable attenuators provide high

attenuation than the attenuators proposed in the literature by John Penn (2005)

and Frank Ellinger and Werner Batchtold (2002).

The simulation results of the vector modulator for various control

voltages at different frequencies with JFET and MOSFET are given in Table

6.7 and the various S-parameters like insertion loss (S21), input return loss

(S11) and output return loss (S22) for the variable attenuators are given in

Table 6.8.

Table 6.7 Simulation results of Vector modulator with JFET and

MOSFET

Phase shifts in degrees for

different Center frequencies for

JFET

Phase shifts in degrees for

different Center frequencies

for MOSFET

Control

voltage

(Volts) 902.5

MHz

947.5

MHZ

2.4

GHz

902.5

MHz

947.5

MHZ

2.4

GHz

1 157.565 157.723 157.614 -88.303 -95.696 -156.429

2 163.491 163.648 163.522 -91.104 -98.517 -157.069

3 169.741 169.896 169.760 -91.735 -99.129 -157.185

4 174.987 175.137 174.997 -92.024 -99.405 -157.233

5 179.102 179.248 179.106 -92.179 -99.554 -157.261

6 -177.719 -177.577 -177.720 -92.266 -99.640 -157.278

7 -175.251 -175.113 -175.256 -92.314 -99.690 -157.291

8 -173.313 -173.178 -173.321 -92.340 -99.719 -157.301

9 -171.768 -171.636 -171.778 -92.352 -99.735 -157.309

10 -170.519 -170.389 -170.530 -92.221 -99.644 -157.378

147

The S-parameters of the vector modulator show that the input

return loss and output return loss are low and the insertion loss is also very

low. For the circuit to be unconditionally stable, Rollette Stability factor (K)

must be greater than 1, the Edward-Sinsky stability factor (µ) must be greater

than 1 and Stability Measure ( ) must be less than 1. From Table 6.8, it is

inferred that the value of K is >1, µ>1and <1 for the vector modulators

implemented with all center frequencies are unconditionally stable.

Table 6.8 S-parameters of vector modulator

902.5MHz 947.5MHz 2.4GHzS

parametersJFET

(dB)

MOSFET

(dB)

JFET

(dB)

MOSFET

(dB)

JFET

(dB)

MOSFET

(dB)

S11 -16.296 -22.799 -16.352 -13.373 -16.248 -14.653

S21 -6.534 -6.087 -6.528 -5.565 -6.528 -3.498

S22 -14.394 -25.106 -14.368 -25.609 -14.398 -15.366

Rollette

Stability

factor (K)

2.257 2.135 2.253 1.858 2.254 1.287

Stability

Measure ( )0.925 0.942 0.924 0.963 0.925 0.971

Edward-

Sinsky

Stability

factor (µ1)

2.594 3.190 2.589 2.268 2.594 1.630

VSWR 1.362 1.156 1.365 1.546 1.364 1.453

The VSWR is greater than 1 for all vector modulators. The AC

simulation is performed to find the Noise Figure (NF) and Signal to Noise

Ratio (SNR) of the vector modulator. For the circuit to have high noise

immunity the NF must be low and SNR must be high. The NF and SNR for

148

the vector modulators are given in Table 6.9. The noise figure of the proposed

vector modulators are less than the noise figure of vector modulators

proposed in the literature by Jesus Grajal et al (1997) and Frank Ellinger et al

(2000). The SNR is very high for the proposed vector modulators.

Table 6.9 NF and SNR of the Vector Modulators

902.5MHz 947.5MHz 2.4GHz

Parameters JFET

(dB)

MOSFET

(dB)

JFET

(dB)

MOSFET

(dB)

JFET

(dB)

MOSFET

(dB)

NF (dB) 2.827 4.860 2.824 3.636 2.820 2.450

SNR (dB) 79.445 76.677 79.440 77.185 79.445 79.713

6.5 CONCLUSION

The vector modulators are implemented with Hybrid coupler,

variable attenuator and Wilkinson splitter as the basic elements and their

performance is studied. The simulation results show that the vector

modulators can work for different control voltages from 1V to 10 V whereas

the vector modulator in the literature works for control voltage of 1.25V to

2.5V (Frank Ellinger et al 2000). The hybrid coupler implemented splits the

input signal into in-phase and Quadrature components with equal power. The

Wilkinson combiner used to combine the in-phase and Quadrature signals

from the variable attenuators combines the signals with minimal loss.

The variable attenuators control the amplitude of in-phase and

Quadrature signals and provide necessary phase shift when connected with

Wilkinson combiner and hybrid coupler. The attenuators provide an

attenuation of 11dB to 20dB for various frequencies. The attenuator in the

literature provides attenuation from 0.6dB to 17dB. The vector modulators

149

implemented are capable of producing phase shift of the signal from 0-360°

for various control voltages. The vector modulators with JFET as control

element in variable attenuator give large phase shifts and the vector

modulators with MOSFET as control element give small phase shifts of the

input signal. Hence the vector modulators with MOSFET can be used in

beamforming systems where the signal is to be steered with small phase shifts

and the vector modulators with JFET can be used in beamforming systems

where the beam has to be steered with large phase shifts.