Thesis organization

This thesis discusses about the front-end circuits design and implementation for WLAN frequency band. The contents consist of two major topics: “A 0.18µm CMOS 5.25 GHz sub-harmonic mixer” and “A 0.18µm CMOS concurrent dual-band receiver front-end”, respectively in Chapter 2 and Chapter 3. We will present the design flow and experimental results. Here is the organization of this thesis.

In Chapter 2, we present the design and implementation of a sub-harmonic mixer.

Here we introduce the fundamental and design flow of the mixer. We will also illustrate the consideration for PCB measurement.

In Chapter 3, a concurrent dual-band receiver front-end consisting of a differential concurrent dual-band LNA, a Gilbert mixer, and a sub-harmonic mixer is designed and implemented. The simulation and measurement results comparison is in section 3.3.

In Chapter 4, we make the conclusion and then present the future prospects.

Chapter 2

S ^UB -H ^ARMONIC M ^IXER U ^SING 0.18µm CMOS

Mixer is a key building block in a communication system that performs frequency translation for down-conversion or up-conversion. Modern wireless communication systems demand stringent dynamic range requirements. The dynamic range of a receiver is often limited by the first downconversion mixer. This forces many compromises between figures of merit such as conversion gain, linearity, dynamic range, noise figure and port to port isolation of the mixer. Integrated mixers become more desirable than discrete ones for higher system integration with cost and space savings. In order to optimize the overall system performance, there exist a need to examine the merits and shortcomings of each mixer feasible for integrated solutions.

In Chapter 2, we introduce the basics of mixers and some indices to evaluate a mixer.

2.1 Mixer Fundamental

2.1.1 Principles of Frequency Translation

The basic idea to generate an output frequency component that is absent from the input port is to multiply two signal of different frequencies. It can be expressed as

(

^cos

)(

^cos

)

^cos

( )

^cos

( )

ω^RF ω^LO = AB2 ⎡⎣ ω^RF +ω^LO + ω^RF −ω^LO ⎤⎦

A t B t t t (2.1)

From the above equation, the multiplication of two signals at the frequency ω_RFandω_LOproduce signals at the frequency

(

^ωRF^+ωLO

)

and

(

^ωRF^−ωLO

)

. Therefore, we can obtain the up-converted and down-convertedω_RF ±ω_LO frequencies.

2.1.2 Topology

Generally speaking, the mixer can be basically categorized as single-balanced and double-balanced types.

(a) (b) Fig. 2.1 (a) Single-balanced mixer (b) Double-balanced mixer

Fig. 2.1(a) shows a single-balanced mixer which accommodates a differential LO signal and a single-ended RF signal. The single-balanced mixer can eliminate effectively feedthrough of the RF signal to the IF signal, which can lead to finite even-order distortion. But the mixer has a main disadvantage that is the LO-IF feedthrough. If the IF frequency is lower than LO, the LO signal can be filtered out by IF filter easily. Fig. 2.1(b) shows a double-balanced mixer that operates with both differential RF and LO inputs. This mixer has several interesting features such as high

conversion gain, low LO power, good isolation, and monolithic integration capability.

Due to these attractive features of the double-balanced mixer, this mixer is most popular topology of active mixer in RF applications.

A. Single-Balanced Mixer

The single-balanced mixer offers a desired single-ended RF input for ease of application. The mixer comprises a common-source stage (M1) and a differential switching quad (M2 and M3). In Fig. 2.1(a), we assume that the mixer under large LO driver and the mixer commutates the RF transconductance current with a square wave.

Referring to Fig. 2.1(a), suppose a unit sinusoidal input voltage of frequencyω_RFis linearity converted to a current, and commutated by the switched atω_LO, which amounts to multiplying the sinusoidal current by a square wave,sq

(

^ωLOt

)

, alternating between +1 and -1. Then the differential current of R_L loads is

where gm1 is the transconductance of M1.

If low-side mixing (LO frequency is lower than RF frequency) is used, (ω_RF −ω_LO) and (ω_RF+ω_LO) terms are the wanted and unwanted signals, respectively.

Eq. (2.2) shows a current conversion loss of at least 2

π through this mixer.

Consequently, the conversion gain therefore can be obtained as

1

2

=π _{m L}

Conversion Gain g R (2.3)

Now, if we consider the switching time of transistors M2 and M3, we can re-express Eq. (2.3) as to the desired conversion gain. Choosing RL, we must tread off the linearity and the conversion gain of the mixer.

The switching quad should be driven by a large LO signal to minimize its noise contribution when all transistors (M2 and M3) are active. The reason is that larger LO voltage swing is needed to turn off one side of the FET switching quad. Besides, linearity, and power consumption considerations set the upper limit on the LO amplitude. A very large LO amplitude results in excessive current being pumped into the source edges of the switching quad through the gate-source capacitance and thus generates additional IM3. Larger LO amplitudes also decrease the voltage headroom at the mixer output. Another disadvantage of using large LO amplitude is the increased power consumption. In brief, is shown in Fig. 2.2, the choice of the LO amplitudes is very important to the mixer design. There exist different optimum LO powers for the conversion gain and noise figure. Through simple in design, it can achieve a moderate gain and low noise figure. However, the design has low P1dB, low port to port isolation, and low IIP3.

LO Power due to its harmonics

distortion due to the harmonics

of the LO signal

(a) (b) Fig. 2.2 Optimum LO power considering (a) conversion gain (b) noise figure

B. Double-Balanced Mixer

Fig. 2.1(b) shows the basic circuit topology of a double-balanced or Gilbert-type mixer. The mixer is consisting of a differential-pair driver stage (M1 and M2) and a differential switching quad (M3~M6). It is important that M1 and M2 and M3~M6 are matched, respectively, for the symmetric purpose. The Gilbert-type mixer is desirable for high port to port isolation and spurious output rejection applications. It can provide high gain and very low noise figure, and the linearity is reasonably good.

In addition, it has the advantage of rejecting the strong local oscillator (LO) component and the even-order distortion products.

The sources of the differential pair for the RF inputs are connected to ground. It is found that a differential pair with a constant current source shown in Fig. 2.3(a) generates higher IM3, than that of a grounded source pair shown in Fig. 2.3(b) biased at the same current. This can be explained by writing down their differential current equations as follows [11].

M

₁

M

₂ Fig. 2.3 Differential pair with (a) constant current source (b) grounded source

In Fig. 2.3(a): the transconductance, so there are no IM3 products in the output of the grounded sources differential pair. However, the short-channel effects, such as nonlinear channel-length modulation and the mobility descending with vertical field, may also yield IM3 in reality.

2.1.3 Effects of Nonlinearity

While many analog and RF circuits can be approximated with a linear model to obtain their response to small signals, nonlinearities often lead to interesting and

important phenomena. For simplicity, we limit our analysis to memoryless, time-variant systems and assume

( )

≈α1

( )

+α2 ²

( )

+α3 ³

( )

y t x t x t x t (2.7)

If a sinusoid is applied to a nonlinear system, the output generally exhibits frequency components that are integer multiples of the input frequency. In Eq. (2.7), if ^{cosx t}

( )

^{= A ωt, then}

In Eq. (2.8), the term with the input frequency is called the “fundamental” and the higher-order terms the “harmonics.”

From the above expansion, we can make two observations. First, even-order harmonics result fromα_jwith even j and vanish if the system has odd symmetry, i.e., if it is fully differential. In reality, however, mismatches corrupt the symmetry, yielding finite even-order harmonics. Second, in Eq. (2.8) the amplitude of the nth harmonic consists of a term proportional to Aⁿ and other terms proportional to higher powers of A.

2.1.4 Conversion Gain

A downconversion mixer should provide sufficient power gain to compensate for

the IF filter loss, and to reduce the noise contribution from the IF stages. However, this gain should not be too large as a strong signal may saturate the output of the mixer. Typically, power gain, instead of voltage or current gains, is specified. The reason is that noise figure is a power quantity, and hence it is easier to translate the NF of the IF stages to the system NF using power gain. Power gain (G) is related to voltage or current gain by

2 2

whereV and_O V are output and input voltages, respectively;_I I and_O I are output and _I input currents, respectively; R and_L R are load and source resistance, respectively. _S Although increasing the load resistance by a factor of 2 can increase the voltage gain by 6 dB, the power gain is increased by only 3 dB.

2.1.5 Intermodulation

For nonlinear circuits such as mixer having multiple non-commensurate small-signal excitations, the nonlinearities in these circuits are often so weak that they have a negligible effect on their linear responses. In view of these references, the 1dB compression point can be computed by taking the ratio of all harmonic terms to it linear term and setting the ratio equal to -1dB (0.891). The IIP3 can be computed by equating the amplitude of the third-order intermodulation products terms with linear term [12]. Fig. 2.4 shows the nonlinear model of the transconductor stage to derive the nonlinearity equations for the single-balanced mixer.

Fig. 2.4 Nonlinear model of transconductor stage in single-balanced mixer

Using the model in Fig. 2.4, Kirchhoff’s voltage law yields:

( )( ) ( )

= + + + + +

s g g gs gd gs s gs m gs ds

V Z R I I V Z I g V I (2.10)

where ₌

(

^{+ −}

)

_{, = − +}

(

^{+ −}

)

+ +

ds gd gs d m gs ds gd gs d m gs

ds gd m gs d

ds gs ds gs

g sC V I g V g sC V I g V

I I g V I

g sC g sC

Using this relationship and Volterra series expression of Id, the Volterra series coefficients are decided. From the Volterra series coefficients, the magnitude of output signal component at frequency 2ω ω₂− or ₁ 2ω ω₁− ₂ determine the input-referred third-order intermodulation product (IM3) which also depends on

(

1

) (

1

)

1+ j Cω ^gs⎡⎣Z^s ω,L^s +Z^g ω ,L^s ⎤⎦ (2.11)

Where the inductive degeneration j C Zω _{gs s}

(

ω1,L_s

)

is a negative real number which cancels the ‘1’ term partially. There is no such cancellation with resistive degeneration since the j C Zω _{gs s}

(

ω1,L_s

)

term is a positive imaginary number, which adds to the imaginary part of the j C Zω _{gs s}

(

ω1,L_s

)

term in Eq. (2.11). For the same reason, capacitive degeneration would increase the IM₃ sincej C Zω _{gs s}

(

ω1,L_s

)

is a positive real number which adds to the ‘1’ term in Eq. (2.11). Therefore, increasing the inductive

source impedance will improve the IM3 and IIP3. The similar analysis for the double-balanced mixer is presented in [12].

2.1.6 Noise

Noise is presented in all transistors making up an active mixer operation [13].

The noise contribution of the loads, transconductor, and switches is presented. More accurate analytic methods have been represented in [14].

A. Load Noise

Flicker noise in the loads of downconversion mixer interfere the signal in a zero-IF or low-IF receiver. PMOSFET has lower flicker noise than NMOSFET [15]

[16]. Using resistors, which are free of flicker noise, need expense of voltage headroom.

B. Transconductor Noise

In Gilbert mixer, the lower transistor, which likes the input stage of RF terminal and translates RF voltage signal to current, is called transconductor stage. Noise in this transconductor transistor is unconverted toω_LOand its even harmonics. And white noise atω_LOand its even harmonics is downconverted to DC. So near DC, the transconductor FET only contribute white noise after frequency conversion.

C. Direct Switch Noise

Without loss of generality, consider the single-balanced mixer in Fig. 2.1(a). In LO switch transistors, VOV ^{> 2}

(

VGS⁻Vt

)

can almost fully switch the current.

Assume there is low frequency noise Vn at the gate of the switch. The waveform of mixer output approach a square-wave at frequencyω_LO, the output superposed with a

pulse train of random width∆tand amplitude of 2I at a frequency of 2ω_LO, suppose the amplitude of the output waveform is I. Over one period the average value of the output current is

where T is the period of LO and S is the slope of the voltage at the switching time [13].

For a sine-wave LO,S T× =4πA, where A is the amplitude and a factor of two accounts for the fact that Vn is compared to a differential LO signal with an amplitude of 2A. For the Eq. (2.12), it means that low-frequency noise at the gate of switch, Vn, appears at the output without frequency translation, and corrupts a signal downconverted to zero IF.

D. Indirect Switch Noise

The flicker noise at the mixer output may be eliminated if the LO waveform is a perfect square-wave with infinite slope at zero crossing. However, as the LO slope decreases, output flicker noise appears via another mechanism that depends on LO frequency and circuit capacitance. This is called the “indirect” mechanism. More accurate analytic about indirect switch noise have been presented in [13].

2.1.7 Port Return Loss

When the port impedance is not matched to that of the source resistance, some of the power delivered to the port is reflected back to the source. Return loss is defined as the fraction of incident power reflected. The impedance of the RF and LO input ports is typically matched to 50 Ω, while the impedance of the IF output port is matched to that of the IF filter. Impedance matching at the RF and IF ports is

necessary to avoid signal reflection and excessive passband ripple in the frequency responses of the filters. Typically, return losses of less than -10 dB are required. On the other hand, the return loss specification on the LO port can be more relaxed.

However, excessive return loss requires the LO to deliver high power which would increase the power consumption of the overall system. Furthermore, excessive LO signal reflected back to the LO may cause LO-pulling problem.

2.1.8 Port Isolation

The isolation between LO and RF ports of the mixer is important as LO-to-RF feedthrough results in LO signal leaking through the antenna. The leaked LO signal should be small enough to avoid corrupting the desired signals of other RF systems.

LO-to-IF and RF-to-IF isolations are not important because the high-frequency feedthrough signals can be rejected by the high-Q IF filter easily. However, large LO and RF feedthrough signals at the IF output port may saturate the IF output port, and decrease the P1dB of the mixer.

2.2 Design of Sub-Harmonic Mixer

2.2.1 Architecture and Circuit Design

Fig. 2.5(a) shows the schematic of the double-balanced sub-harmonic mixer.

This design approach is based on the classical Gilbert mixer with a switching quad that can conduct on each half cycle of the driving waveform. Since the double-balanced structure has the advantages of high gain, low noise, good linearity, and high port-to-port isolation compare with the single-balanced structure, we adopt the double-balanced structure in this design. In Fig. 2.5(a), the transistors M1-M2 form

the input transconductor, which convert input RF voltage signal into current signal.

Then the current signal is delivered to switching quad, which is turned on and off current signals by the local oscillator signal. Finally, such switching activities perform multiplication of the RF current signal with the local oscillator signal. This multiplication relies on the square law of voltage-current relationship to achieve the frequency-translation. Although the series resistors consume valuable dc voltage headroom, they have the performance of the free flicker noise. As a result, we use series resistors as the loading in this design. From section 2.1.2, we can know that a differential pair with a constant tail current exhibits higher-order nonlinearity than grounded source. To improve linearity, the differential input transconductor was realized as a grounded source differential pair. In addition, we match RF port to 50Ω by on-chip pi-matching network.

The sub-harmonic LO switching quad consists of M3-M10 as shown in Fig. 2.5(a).

When operating with LO signals with large amplitude, the LO switching quad acts as a mixer by commutating the load across the drains of the input transconductor stage at twice the LO input frequency. Unlike a Gilbert mixer, however, the mixer topology relies on the phase relationship of the LO signals to provide a region where the 0/180∘ and 90/270∘ devices are both off to create the effective twice LO switching frequency. The quadrature signal (about half of RF frequency) applied to the LO inputs allows the RF signal to be switched on every quarter cycle of the LO drive waveform, creating an effective 2fLO signal. Fig. 2.6 shows the waveforms within the mixer driven by a quadrature LO input without RF drive. From Fig. 2.6, we can visualize the effect of the LO signal in creating the doubled LO frequency internal to the mixer. The size and gate-source bias voltage of the switch transistors should be optimized in view of switch noise, gain, and LO amplitude requirement. For

low-noise operation, the size of the switch should be large; however, it inevitably leads to large parasitic nonlinear capacitance at the midpoints of the transconductor and switching quad, introducing signal loss in these nodes and degrading linearity.

The optimum gate-source bias of the switch is slightly below the threshold voltage of the NMOSFET. Actually, the switching quad is designed to operate in the weak inversion region to reduce flicker noise.

For measurement purpose, we connect an on-chip common-drain output buffer as shown in Fig. 2.5(b) to simultaneously match IF port to 50Ω and increase output driving capability. Finally, we take advantage of the pi-matching circuit as shown in Fig. 2.5(c) to match LO port to 50Ω and be able to provide sufficient LO power from outside signal generator to mixer.

(a)

(b)

(c)

Fig. 2.5 (a) Double-balanced sub-harmonic mixer (b) Common-drain output buffer (c) Off-chip matching network of the LO port

Fig. 2.6 Operation of double LO frequency

2.2.2 Design Flow

In this section, we attempt to systemize the design step of the sub-harmonic mixer.

The current and the minimum overhead voltage are utilized to determine the transistor size and DC bias of the transconductor. The goal in this step is to ensure that the transistor works in saturation region, given a certain variation range for its drain voltage. As discuss in previous sections, noise figure, conversion gain, and linearity are all related to the sizes of the transconductor transistors. Conversion gain and linearity are major consideration initially, but noise figure should be refined later.

The variation range of the drain voltage of the transconductors is determined by taking in account the variation caused by the LO switching activities. It is now time to determine the LO bias voltage and the size of the switching quad. Non-ideal switching behavior, that is, the switches are not completely turned on or off, will reduce the conversion gain, and possibly generates more noise. Similar to the transconductors, the switching quad is designed to work in saturation region, taking the variation of the gate source voltage and the drain voltage into consideration. Note that the preferred variation range of the drain voltage of the switching quad is much larger than that of the transconductor; because we want the IF signal to vary over a large voltage range without causing distortion.

The matching network of the RF port, LO port, and IF port can now be determined for maximum power transmission. In case noise performance cannot be satisfied, the RF port should be matched for optimal noise figure.

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