Noise and Noise Reduction Techniques in Gilbert Mixer Design

Unlike in the LNAs, the noise figure definition in the mixer is often confused due to the existence of the image signals. The image signal and the expected signal are also called sidebands in mixers. The SSB is assumed to be the only noise from the expected signal frequency and not the image frequency, but the DSB evaluates both sidebands as a result of twice as much power available at the IF port compared to the SSB signal.

However, the intuitive view of the noise in the mixer includes both the flicker and the thermal noise dominating the separate frequency bands as is the situation in LNAs. At low frequency, the flicker noise at the trans-conductors appears in down-conversion mixing, which translates the flicker noise to ߱_ܮܱ and its harmonics. Due to the

(3-85)

(3-86)

mismatch of the switching, small amount of flicker noise appears in the output without frequency translation. In addition, the IF loads will also contribute a certain amount of flicker noise. Therefore, PMOS load is preferred in some designs since it has less flicker noise as compared to an NMOS load[151]. Even if the switches perform perfect switching at the zero-crossing, the noise voltage that is superimposed onto the ߱ܮܱ

signal affects the switching time[152]. The flicker noise will add current impulses with amplitude of ʹܫ at a frequency ʹ߱_ܮܱ with a pulse train of random widths change in switching timeοݐ. The average value of the output current over one LO period (ܶ_ܮܱ) is

݅_݋ǡ݊ ൌ ʹ

ܶ_ܮܱൈ ʹܫൈοݐൌ Ͷܫ ݒ݊

ܵܶ_ܮܱ

Where, ܵ is the slope of the LO at the zero-crossing. From the expression, it is clear that the switch flicker noise appears at the output without any frequency translation and it decreases when the slope increases and/or the bias current decreases. The zero-crossing modulation,οݐ, depends on the low-frequency noiseݒ_݊ and the voltage slope ܵ can be increased by enlarging the LO power. Secondly, increasing the gate area of transistor in the mixing stage can also reduce theݒ_݊.

RL VDD

V

C

I

v

V

M

M

Figure 3-18: Single-balanced mixer with switch noise

From an indirect point of view, the output flicker noise appears via another mechanism, which depends on the LO frequency and the circuit tail capacitorܥ_ݐ݈ܽ݅[152]. ܥ_ݐ݈ܽ݅ is

charged up exponentially by the noise voltage during half of the cycle with the same frequency as LO. The output noise current therefore can be expressed as:

݅݋ǡ݊ ൌ ʹܥ_ݐ݈ܽ݅

ܶܮܱ ȉ ݒ݊ ȉ

ሺ߱_ܮܱܥ_ݐ݈ܽ݅ሻʹ

݃݉ʹ൅ሺ߱ܮܱܥݐ݈ܽ݅ሻʹ

Therefore, when tail capacitance dominates, flicker noise can be reduced by using larger switching transistors, which have large LO power. If the capacitance is dominated by the switching trans-conductor’s junction (݃_݉) capacitance, larger switch size can lower the flicker noise.

At high frequency, the noise still involves the same three source from the switches, the IF loads and the trans-conductors. The thermal noise of the switches can be referred to as the differential. The sampling function of impulse train can be given by

݌ሺ߱ܮܱݐሻൌ෍ ܩ݉൬ݐ െ

݊ܶܮܱ

ʹ ൰

݊

where switching trans-conductanceܩ_݉ have a period twice of the LO frequency, since there are two zero-crossing over at each LO cycle. The mixer output current thus yields to

݅_݋ǡ݊ ൌ݌ሺ߱_ܮܱݐሻ ȉ ݒ_݊ሺݐሻ

which appears as white noise and cyclostationary characteristic. When the LO waveform is a sine-wave with slopeܵ equal to twice of LO amplitude (ܣ_ܮܱ), the power spectral density of the noise current at the output due to one switch is

ห݅_݋ǡ݊หʹ

തതതതതതതത_{ൌ Ͷ݇ܶߛ} ܫ

ߨܣ_ܮܱ

Expression 3-92’s output is dependent on the bias current and LO amplitude and demonstrates that there is no effect of switch size when ܥ_ݐ݈ܽ݅ is negligible. In Practical applications, large ܥ_ݐ݈ܽ݅ does affect the gain of the mixer at high frequency.

(3-89)

(3-90)

(3-91)

Nevertheless, it increases the noise figure since direct translation causes the drain noise current flow into a finite ܥ_ݐ݈ܽ݅ impedance when only one switch is “on”. Furthermore, the thermal noise of the trans-conductors around each odd order harmonic of the LO signal translates to IF similar to the RF signal [153]. Noticeably, the thermal noise around the even order harmonic is cancelled out in balanced topology. Therefore, the Gilbert mixers produce large amount of noise.

A number of different techniques are proposed to reduce both the flicker noise and the thermal noise. As discussed, the switches contribute most of the flicker noise; therefore, in order to reduce flicker noise of the switches, both large LO power and low overdrive voltage can be used. The current bleeding techniques are widely adopted for Gilbert mixers to maintain high conversion gain and minimum bias current for the mixing stage [154-158]. The current bleeding is also known as charge-injection method that provides extra current for the trans-conductance stage, as shown in Figure 3-19. Most of the RF signal will be forced into entering switching pairs since current source has large output impedance. However, the drawback of the current source is an increment in the tail capacitance, which amplifies the flicker noise indirectly. This issue has been discussed and resolved in the literature [155, 156]. The same method of using inductor degenerated topology in LNA design can be applied here by resonating out the tail capacitance to reduce the flicker noise. Therefore, the current bleeding technique and inductor degenerated topology is often used simultaneously to reduce overall flicker noise and enhance conversion gain for the mixer.

VLO+ VLO- VRF+ M1 M2 VRF- VDD VDD RL RL M3 M4 M5 M6 VIF+ VIF- VLO+ VDD VDD

In terms of the thermal noise, trans-conductors contribute the majority of it. Thus, this noise can be reduced significantly by replacing the trans-conductors with the proposed

LNA’s topology, as discussed previously. Current bleeding technique also reduces the noise contribution of the switching stage since the DC current gets smaller.