Principle of Mixers

The mixer is an ubiquitous component of wireless systems. An ideal mixer multiplies the signal at the radio frequency (RF) port with a signal at the local-oscillator (LO) port to create the intermediate-frequency (IF) signal. If the RF and LO signals are sinusoids, it is clear that the IF signal has components at two frequencies. There is a high frequency component at the sum of the RF and LO frequencies, and a low frequency signal at the difference of the RF and LO signals.

Therefore, a mixer can effect up conversion or down conversion [5]. In design of RF CMOS mixers is a very challenging task involving trade offs between gain, linearity, noise figure, voltage supply and power consumption.

2.3.1 Conversion Gain

One important mixer characteristic is conversion gain, which is defined as the desired IF output

Conversion Gain=

the value of the RF input (2-19) The gain of mixers must be carefully defined to avoid confusion. The “voltage conversion gain” of a mixer is defined as the ratio of the rms voltage of the IF signal to the rms voltage of the RF signal. Note that these two signals are centered around two different frequencies. The voltage conversion gain can be measured by applying a sinusoid at ω and examining the amplitude of the downconverted component at ^RF ω . IF

The “power conversion gain” of a mixer is defined as the IF power delivered to the load divided by the available RF power from the source. If the input impedance and the load impedance of the mixer are both equal to the source impedance, for example, 50Ω, then the voltage conversion gain and power conversion gain of the mixer are equal when expressed in decibels.

Conjugate matching at the input of the mixers is necessary in the first downconversion stage of heterodyne receivers that employ image reject filters. The transfer function of these filters is usually characterized for only a standard termination impedance and may exhibit ripples if other impedance levels are used.

The load impedance of the mixer, on the other hand, is typically not equal to 50Ω because most passive IF filters have an input impedance of 500 to 1000Ω. In architectures such as homodyne topologies, the load seen by the mixer may be even higher to maximize the voltage gain.

From the above observation, we note that the voltage and power conversion gains of a mixer may not be equal in decibels.

2.3.2 Noise Figure : SSB and DSB

Noise Figure is defined as

signal to noise ratio at RF port Noise Figure=

signal to noise ratio at IF port (2-20) In a typical mixer, there are actually two input frequencies that will generate a given intermediate frequency. One is the desired RF signal, and the other is called the image signal. The existence of an image frequency complicates noise figure computations because noise originating in both the desired and image frequencies therefore becomes IF noise, yet there is generally no desired signal at the image frequency. In the usual case where the desired signal exists at only one frequency, the noise figure that one measures is called the single-sideband noise figure (SSB NF); the rarer case, where both the “main” RF and image signals contain useful information, leads to a double-sideband (DSB) noise figure. Clearly, the SSB noise figure will be greater than for the DSB case, since both have the same IF noise but the former has signal power in only a single sideband. Hence, the SSB NF will normally be 3dB higher than the DSB NF.

2.3.3 Isolation

Isolation is one of another parameter in design mixer. It is generally desirable to minimize interaction among the RF, IF, and LO ports. For instance, since the LO signal power is generally quite large compared with that of the RF signal, any LO feedthrough to the IF output might cause problems at subsequent stages in the signal processing chain. This problem is exacerbated if the IF and LO frequencies are similar, so that filtering is ineffective. Even reverse isolation is important in many instances, since poor reverse isolation might permit the strong LO signal to work its way back to

the antenna, where it can radiate and cause interference to other receivers.

2.3.4 Single Balanced and Double Balanced Gilbert Mixer

Fig. 2.4 Single Balanced and Double Balanced Gilbert Mixer

The circuit of single balanced and double balanced Gilbert mixer is shown in Fig. 2.4.

The lower stage is operated as a transconductance amplifier which converts RF voltage into a current and then performs a multiplication in the current domain. VLO

is chosen large enough so that the transistors alternately switch all of the tail current from one side to the other at the LO frequency. In single balanced mixers, the output consists of sum and difference components, each the result of an odd harmonic of the LO mixing with the RF signal. It makes the linearity worse. So the double balanced mixers exploit symmetry to remove the undesired output LO component through cancellation. Double balanced mixers make the linearity better than single balanced mixers.

In the low voltage applications, the DC current source can be replaced by a parallel LC tank to create a zero headroom AC current source. The resonant frequency of the tank should be chosen to provide rejection of whatever common mode component is most objectionable. If several such components exist, one may use series combinations of parallel LC tanks.