Design of 1.9 GHz Gilbert-Cell Down-Conversion Mixer With good linearity in 0.18 µm CMOS Technology

* K. Faitah, ** R. Mahmou

* Laboratory of Electrical Engineering and Control Systems (LGECOS).

Department of Electrical Engineering, National Institute of Applied Sciences (ENSA).

Cadi Ayyad University, Marrakech, Morocco.

Avenue Abdelkrim El Khattabi P.O box: 575 Marrakech Morocco.

E-mail (faitah.khalid@gmail.com)

**Laboratory Of Electrical Engineering and Control Systems (LGECOS).

Department of Electrical Engineering, National Institute of Applied Sciences (ENSA).

Cadi Ayyad University, Marrakech, Morocco.

Avenue Abdelkrim El Khattabi P.O box: 575 Marrakech Morocco.

E-mail (rajae.mahmou@yahoo.fr)

Abstract This paper describes the design of a double balanced mixer known as a Gilbert cell mixer.

The proposed design, which operates at a radiofrequency (RF) of 1.9 GHz, is implemented in

0.18 µm CMOS technology at a supply voltage of 1.8 V. The components values and the size of

CMOS transistors used to achieve a better linearity while keeping a good conversion gain are

calculated. The obtained results show a third order input intercept point (IIP3) and an 1-dB

compression point in the order of 10.5 dBm and -2 dBm, respectively when the conversion gain

roughly equal to 9.12 dB. These performances justify the good linearity of the mixer compared to

those using an inductive degeneration or active loads like P-channel MOS.

Key words Mixer, Gilbert cell, degeneration resistor, conversion gain, linearity.

1. Introduction The CMOS technology has now reached its maturity by its very high integration degree. The

choice of CMOS technology allows not only to benefit, at the present time, from the lowest price

in the semiconductors market, but also from manufacturing circuits in very large quantities and in

a controlled manner. The performance improvements of this technology allow to develop

products operating in the 1-8 GHz frequency band for broadband applications [1][2].

Despite this growth, the MOS transistor presents one of the lowest ratio current/gate width.

This has a direct influence on the transistor’s gain through its transconductance. On the other

hand, an important feature of the silicon substrate is that it is a semiconductor unlike the gallium

arsenide which is semi-insulating. This property leads losses in the substrate through parasite

capacities. So, magnetic fields introduced into the substrate may cause adverse currents. The low

substrate resistivity generates significant current contrary to very resistant substrates. Thus, there

are phenomena of interference, "cross talk" and "noise coupling", between the signals which can

be mitigated through a differential architecture, such as that adopted by the Gilbert cell,

eliminating the maximum of common mode.

The mixer is an essential block in any telecommunication system which has a critical impact

on the performances of all system functions. It is an analog multiplier, as shown in Figure 1,

which allows a time multiplication of two signals, the first one (RF signal) comes from the

receiver antenna after has been filtered and amplified, and the other signal (LO signal) comes

from a local oscillator [3].

Fig.1. RF receiver building blocks.

2. Architecture of proposed Gilbert mixer Although it has enough advantages, the single balanced mixer (SBM) is limited in terms of

linearity; its conversion gain is constant only for the weak input powers. The circuit that we will

present in Figure 2 will improve the linearity of the mixer, maintaining a low noise and a good

conversion gain. Indeed, it is composed of three differential pairs (M2, M3), (M4, M5) and

(M6, M7): each is composed of two identical transistors, all connected to a current source based of

transistor M1.

Generally, the differential pairs are intended for the acquisition of the voltages by

converting the difference of their input voltages in a current, circulating thus on a load and

converted into voltage. [4], [5].

2.1 Principle of the mixer architecture The RF pair (M2, M3) provides the gain. It consists of two common-source transistors, M2

and M3 that convert the differential input voltage in differential current. The range of differential

voltage Vid, for which the two transistors (M2, M3) are active at the same time, depends on both

the geometrical dimensions (W, L) and the generated current IG through transistor M1.

The currents I2, and I3 are then routed to two differential pairs (M4, M5) and (M6, M7)

controlled by a strong LO signal so that they operate in switching mode [6]. Such a commutation

block is the core of the circuit where RF and LO signals are mixed. Finally, the total current I0 is

converted into a voltage output IF (Vo1 - Vo2) by a load (Rload). The Figure 3 summarizes the

operating principle of this cell.

.

M4

.

M 5

I3

Vcc

I2

Rload Rload

M1

M 7

IG

M 3

.

Differential LO Input

M6

Tail current bias adjust

Io3

.

Io2

Vcc

Differential IF Output

.

Differential RF Input

Vee

.

M2

Fig.2. Gilbert cell mixer. Fig.3. Operating principle of the

Gilbert Cell.

2.2 Design of MOS transistors This is the most important phase in this work; it is to determine the approximate values of

the mixer components. Then, an adjustment will be made after the simulation to achieve the

desired performances. The width of input RF transistors block is determined, using a technique

based on the minimum noise to obtain optimal size of the width that is expressed by [7]:

oxsopt CLR

WW3

1 (1)

where W and L are respectively the width of the active zone of the transistor and the

minimum length of the used technology. Cox is the surface capacitor of the gate-channel and Rs is

the resistor of matching, generally equal to 50 Ω.

230 /10463.8 mFt

KCox

oxox

(2)

where εo the absolute permittivity, Kox is a constant equal to 3.9 and tox is a gate oxide

thickness. The pulsation ω, in the case of an operating frequency equal to 1.9 GHz is:

ω = 2π f = 11.932 rad/s (3)

We get an optimal width of about 367 µm for the transistors of RF stage.

2.3 Study of linearity The linearity is mainly linked to three main sources: the RF stage, the switching circuit and

the load. The most important source is composed by the RF transistors (M2, M3). Then this

transducer is the pillar of the mixer performances (gain, linearity, noise) and particularly the third

input intercept point (IIP3). Several techniques have been proposed in several publications to

improve the linearity [8] [9] [10]. Generally, the degeneration topology is one of the most often

used for mixers, but at the expense of the surface that is occupied by the significant number of

components, and also at the expense of noise and power consumption comparatively with single

balanced mixers. In this work, we opted for a source degeneration of M1 and M2 by resistor Rs, as

shown in the following Figure 4.

Rs Rs

M 1

M 3

Tail current bias adjust

Differential RF Input

Vee

.

M2

IG.

I3I2

To M4 .. to M7

Fig.4. Circuit with resistive degeneration sources.

By considering the load resistor RD of the RF stage, we can express the equivalent

transconductance of the circuit as [11]:

RF

Dm V

IG

(4)

Assuming GSD VfI , we write:

RF

GS

GSm V

VVfG

(5)

Since DSRFGS IRVV then the expression (5) can be written:

GSRF

DSm V

fVIRG

1 (6)

As GSVf

is the transconductance gm of M1 thus:

(4) and (6) give:

Sm

mm Rg

gG

1

(7)

The signal voltage gain is thus equal to:

Sm

Dmv Rg

RgG

1

(8)

Form

s gR 1

, we have S

m RG 1

then S

RFD R

VI . We can say that the drain current is a

"linear" function of the input voltage.

This constraint will allow us, when the simulation of the circuit takes places, to correctly

calculate the values of Rs and Rload.

3. Simulation results The circuit of the Gilbert cell mixer is shown in Figure 5.

For the purposes of the simulation we need to convert the differential inputs (RF, LO) and

output (IF) of the mixer to single ended source and load impedances. The device that achieves

this balanced to un-balanced transformation is known as a Balun. This differential structure is so

necessary so as to add the LO signals, whose phases are opposed to cancel them. This will avoid

the low IF- LO isolation of SBM. In fact, the differential pair in the case of Gilbert cell operates

as a LO signal amplifier.

Differential IF Output

nRF Input

Ibias

0.6mAdc

Rload = 200

M8

Vdd

M1

Io2

M2

Vdd1.8Vdc

Rload = 200

Io3

R3

10k

R2

10k

nLO Input

I3

M3

LO Input

IG

C210p

Vee = -1.8 V

Vdd

C310p

M6

0

M5

Vdd

Rs

20

Vdd

Rs

20

.

I

.

0

M4

RF Input

I2

0

Tail current bias adjust

0

M7

Fig.5. Gilbert cell mixer under ADS tool.

Using the ADS tool and 0.18µm CMOS technology, the simulation was made with the

transistors size equal to W = 367 µm and L = 0.18µm, the degeneration resistor is equal to

20 and the bias current is of 0.6 mA.

The following graphs show that the proposed circuit realizes the function of mixing

frequencies.

Fig.6. Frequency input signal at 1.9 GHz. Fig.7. Frequency LO signal at 1.8 GHz.

Fig. 8 Output mixer spectrum. Fig.9. Output mixer vs time.

We note that the output shows a frequency value fRF - fLO equal to about 100 MHz.

Nevertheless a carrier at 3.7 GHz plus other unwanted harmonics are due to the non-linearity of

transistors. They can be eliminated, using a filter "to return" only the desired frequency. Being

sure that our circuit design realizes the frequency mixer function, we then simulated the most

relevant parameters to characterize the good functioning of the circuit: the conversion gain Gc,

10 ns

linearity described by the third order input intercept point (IIP3), 1-dB compression point, the 3rd

order intermodulation designated by IM3 and the power consumption.

3.1 Conversion Gain These simulation results are obtained by tuning the RF input power from -30 dBm to

10 dBm, the Figure 10 represents the conversion gain roughly equal to 9.13 dB.

Fig.10. Gain versus RF input power.

3.2 Noise Figure From the intermediate frequency IF = 100 MHz which corresponds to our circuit, the tool

ADS using the appropriate following equations:

Where: Gv = 9.120 = dB and NF and 9.740 dB.

3.3 1-dB compression point This point marks the limit of linear operation of the circuit. In fact, the mixer is subject to the

phenomenon of saturation output power caused by the strong input power. It is defined as shown

in Figure 11, to the point of power for which the gap between power output and its linear

extrapolation reaches 1 dB. We found a value of -2.17 dBm.

Fig.11. Simulation of 1-dB compression point.

3.4 Third order input intercept point (IIP3) To find this point, we did a test using two signals whose frequency is around that of RF.

A simulation with two input signals whose frequencies f1 = 1.905 GHz and f2 = 1.895 GHz, not

far from fRF = 1.9 GHz and with the frequency of local oscillator fLO = 1.8 GHz, we obtain the

spectrum of Figure 12.

Fig.12. Output spectrum around the IF frequency.

By using the relationship [12]:

RFPowerIMIIP _2

33 (9)

We find the following results:

IM3 = m1 - m2

IP3_in = RF_pwr + IM3 / 2

The IM3 has a negative effect when the desired signal at the entrance of the circuit is

accompanied with two strong signals, then it will be affected by the presence of a carrier

intermodulation in the useful channel. In our case, the IM3 value of 60.9 dBm is very good, so

that this phenomenon of intermodulation hardly appears in practice. Also a positive IIP3 value

equal to 10.45 dBm justifies that this circuit can operate in linear system on a wide band powers

of entry.

3.5 Power consumption Pc

ddddc IVP (10)

Idd = 17.1 mA and Vdd = 1.8 V this gives:

Pc = 30.78 mW: power consumption is still at a reasonable level given the number of

components that make up the circuit.

4. Improvement of the conversion gain [8] To improve the conversion gain, the resistive loads of the architecture in Figure 2 must be

replaced by active loads using PMOS as shown in Figure 13.

I2

Rs

20

0

M6

M1

R3

10k

Io2

.

Rs

20

R2

10k

Vee = -1.8 V

M8

Vdd

IG

Vdd1.8Vdc

LO Input

I3

M2

M7

Io3

VddM4

P MOS1

nLO Input

M3

Ibias

0.6mAdc

0

M5

RF InputC310p

0

.

I

nRF Input

Vdd

0

Vdd

P MOS2

Differential IF Output

0

Tail current bias adjust

C210p

Fig.13. The proposed double-balanced mixer topology with p-channel MOS load.

The PMOS improves the gain, but decreases the linearity as explained in section 2.3. We

found:

-25 -20 -15 -10 -5 0 5-30 10

2

4

6

8

10

12

14

0

16

RF_pwr

Gai

nCon

vers

ion1

m7

m7RF_pwr=GainConversion1=14.401

-24.203

Fig.14. Gain versus RF input power (with PMOS load).

-25 -20 -15 -10 -5 0 5-30 10

-15

-10

-5

0

5

10

15

20

-20

25

RF_pwr

dBm

_out

m4

Tang

Line

m4RF_pwr=dBm_out=6.564

-6.812

Fig.15. Simulation of 1-dB compression point (with PMOS load).

Thus Gc = 14.5 dB, 1-dB compression point equal to -6.81 dBm.

After simulation, we find also:

IIP3 = -1.85 dBm and noise factor equal to 9.88 dB.

With inductive degeneration by replacing the resistances R11 and R12 of Figure 2 by inductors

of 15 nH, we obtain a good gain, an eligible noise factor and a linearity slightly better than the

mixer with an active PMOS load:

Gc = 14.37 dB, 1-dB compression point equal to -6.23 dBm, IIP3 = 0.74 dBm and noise

factor equal to 7.79 dB.

The obtained results can be summarized in the table 1.

Parameters Gilbert-Cell with

R degeneration

Gilbert-Cell

with L degeneration

Gilbert-Cell with

PMOS active load

Technology 0.18 µm 0.18 µm 0.18 µm

Voltage supply 1.8 V 1.8 V 1.8 V

RF frequency 1.9 GHz 1.9 GHz 1.9 GHz

LO frequency 1.8 GHz 1.8 GHz 1.8 GHz

Conversion gain 9.12 dB 14.37 dB 14.5 dB

Noise figure 9.74 dB 7.79 dB 9.88 dB

3rd order input

intercept point (IIP3) 10.45 dBm 0.74 dBm -1.85 dBm

1-dB

compression point

-2.17 dBm -6.23 dBm -6.81 dBm

Power

consumption

30.78 mW 30.87 mW 30.96 mW

Table.1. Simulation Results of Three Structures.

It has shown that the proposed circuit in this study is largely better in terms of linearity

although its power consumption is quite high. But it is still acceptable.

5. Post-layout simulation The final size of the mixer layout is 108 µm x 67 µm as described in Figure 16.

The post-layout simulations are illustrated in Figure 17. The results are in agreement with

that obtained using the ADS tool presented above: (The output signals Vout1 and Vout2,

corresponding to IF and nIF, have a frequency exactly equal to 100 MHz).

Fig.16. The layout of the proposed design.

Fig.17. Diagram simulation of input/output of the layout

(The output signal frequency is roughly equal to 100 MHz)

Conclusion In this paper, the most important parameters characterizing the double balanced mixer have

been calculated. The linearity of the mixer has been improved, by means of resistive degeneration

sources of RF stage, which led to promising results. Another technique which uses an inductive

degeneration, to promote less noise and more linearity, has been studied. This technique has a

negative effect on the limitation of the bandwidth. Then, the designer should make a compromise

by choosing between the technology and the desired circuit design, by assuming the advantage of

a technique over the other and vice-versa. The obtained results in this study show that the

proposed mixer could be used for wireless communication for instance in the WLAN

applications.

Acknowledgement The authors would like to thank the professor Etienne Sicard, from LATTIS “Laboratoire

Toulousin de Technologie et d’Ingénierie des Systèmes”, Toulouse, France, for its valuable

contribution in the design of the mixer layout.

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