Image-Reject Receivers

Moitreya AdhikaryM.E. 2nd Semester Dept. E&TC (Microwave)

ID- 210713016Exam Roll- 161307013

Session 2013-14IIEST, Shibpur

Contents• Origin of image problem• Why image-reject receivers?• Image-reject architectures• 90ᵒ phase shift operation• Quadrature mixing operation• Hartley architecture• Image rejection in Hartley architecture• Drawbacks of Hartley receiver• Weaver architecture• Image rejection in Weaver architecture• Advantages of Weaver architecture• Drawbacks of Weaver receiver• Calibration• Conclusion• References

Origin of Image ProblemWhen centre frequencies of the desired input RF spectra and another (image) spectra are located symmetrically about ωLO

and 2ωIF apart from each other, both are down-converted to ωIF leading to the Image problem in heterodyne receivers.

Image-reject filter is employed to alleviate image problem.

Figure1: Problem of image in heterodyne down-conversion

Figure2: Image rejection and channel-selection trade-off in traditional heterodyne receiver (a) high IF and (b) low IF

But Higher ωIF Better Image rejection&Lower channel selection

Why Image-Reject Receivers?

1. "Image-reject" architectures are a class of receivers that suppress the image without filtering, thereby avoiding the trade-off between image rejection and channel selection as in traditional heterodyne and direct-conversion receivers .

2. Traditional receivers employ an explicit image-reject filters to suppress the image before mixing. These filters have high power consumption and require off-chip implementation. Whereas, image-reject receivers are low-power, fully monolithic as no image-reject filtering is required in them.

Image-Reject Architectures

The basic objective of an image-reject receiver is to process and suppress the image-tone without utilizing an explicit, external filter. A useful metric to quantify the degree of image rejection in a receiver is the image rejection ratio (IRR), which is defined by:

Typical wireless standards, such as DCS-1800, require an IRR of 1000 (60dB). In the ideal case, the image signal level is equal to zero, and IRR = ∞.

There are various image reject receiver architectures possible. The most fundamental ones of them are:

1. Hartley Architectureand

2. Weaver Architecture

90ᵒ Phase Shift operation

90ᵒ phase shifter is an essential component in Hartley receiver. Let us graphically look at the effect of 90ᵒ phase shift in case of a tone Acos(ωct) and a narrowband modulated signal A(t)cos[ωct + Φ(t)].

Thus positive frequency contents are multiplied by -j and the negative-frequency contents by +j (if ωc is positive).

Alternatively in frequency domain,X90ᵒ(ω)=X(ω)[ -jsgn(ω)]

where sgn(w) denotes the signum (sign) function. The shift-by-90° operation is also called the "Hilbert transform”. It can be proved that the Hilbert transform of the Hilbert transform (i.e., the cascade of two 90° phase shifts) simply negates the original signal.

Quadrature Mixing Operation

Figure3(a): High-side injection (ωLO >ωC )

Quadrature mixer is another constituent block of image-reject receivers. The effect on signal spectra by the operation of quadrature mixing is shown in Figure3.

(a)

Quadrature Mixer

Signal+ve Hilbert Transform

Figure3(b): Low-side injection (ωLO <ωC)

Thus to summarize, the quadrature converter produces at its output a signal and its Hilbert transform if ωLO >ωC and the negative of its Hilbert transform if ωLO <ωC .

Signal -ve Hilbert Transform

Hartley Architecture

The Hartley architecture is the most basic image-reject architecture where,

• The incoming RF signal is mixed with quadrature outputs of the local oscillator signal, namely sinωLOt and cosωLOt, and fed through a low pass filter.

• The signal at node B (Figure4) is then shifted by 90 degrees by a RC-CR network and signal at node C is then added to the signal at node A.

Figure4: Hartley image-reject receiver

Figure5: Realization of 90ᵒ phase shift

LPF section

HPF section

Image Rejection in Hartley Architecture

How image components cancel each other?

The Hilbert transform of the Hilbert transform negates the signal, this hypothesis forms the foundation for the Hartley architecture.

In summary, the Hartley architecture first takes the negative Hilbert transform of the signal and the Hilbert transform of the image (or vice versa) by means of quadrature mixing, subsequently takes the Hilbert transform of one of the down-converted outputs, and sums the results. That is, the signal spectrum is multiplied by [+jsgn(ω)][-jsgn(ω)]=+1, whereas the image spectrum is multiplied by [-jsgn(ω)][-jsgn(ω)]= -1.

(a)

(b)

Figure6: Image and signal spectra (a) after quadrature down-conversion with low-side injection and (b) after 90ᵒ phase shift

Qim,90ᵒ has opposite polarity of Iim , thus cancel each other out after summation but Isig and Qsig,90ᵒ are additive

Low-side injection

Drawbacks of Hartley Receiver

ϵ

Phase error

There are several drawbacks of Hartley architecture,

1. The principal drawback of the Hartley architecture stems from its sensitivity to mismatches: the perfect image cancellation occurs only if the amplitude and phase of the negative of the image exactly match those of the image itself.

Relative gain error

With various mismatches arising in the LO and signal paths, the IRR typically falls below roughly 35 dB.

2. Another critical drawback, especially in CMOS technology, originates from the variation of the absolute values of R1 and C1 (due to process or temperature variation etc.).For example, R/ R1 = 20% limits the image rejection to only 20dB.

3. Another drawback resulting from the RC-CR sections manifests itself if the signal translated to the IF has a wide bandwidth. Since the gains of the high-pass and low pass sections depart from each other as the frequency departs from ωIF = 1/(R1C1) (Figure7), the image rejection may degrade substantially near the edges of the channel.

Figure7: Frequency response of RC-CR 90ᵒ phase shifter

4. The RC-CR section also introduces attenuation and noise.

5. The voltage adder (usually differential pairs) at the output of the Hartley architecture also poses difficulties as its noise and nonlinearity appear in the signal path.

Weaver Architecture

To alleviate the mismatch problem associated with the RC-CR 90ᵒ shift network in the Hartley architecture, the network can be replaced with a second quadrature mixing stage, which is known as Weaver architecture.

Figure8: Weaver architecture

Image Rejection in Weaver Architecture

The signals at different nodes are given by,

Image is removed

Figure9: Simplified frequency domain signals at different nodes in Weaver architecture

No image

Advantages of Weaver Architecture

1. While employing two more mixers and one more LO than the Hartley architecture, the Weaver topology avoids the issues related to RC-CR networks : (i) Resistance and capacitance variations, (ii) degradation of IRR as the frequency departs from 1/(R1C1), (iii) attenuation, and (iv) noise.

2. Also, if the IF mixers are realized in active form, their outputs are available in the current domain and can be summed directly.

Drawbacks of Weaver Receiver1. The IRR is still limited by mismatches, typically falling below 40 dB. Since

the circuit still depends on the precise cancellation of the image-tone through subtraction, gain and phase mismatches between the signal paths are still a critical problem.

2. The Weaver architecture must deal with a secondary image (Figure10) if the second IF is not zero. This effect arises if a component at 2ω2-ωin+ω1 accompanies the RF signal.

3. The Weaver topology also suffers from mixing spurs in both down-conversion steps. In particular, the harmonics of the second LO frequency may down-convert interferers from the first IF to baseband.

Figure10: Secondary image in Weaver architecture

Calibration

For image-rejection ratios well above 40 dB, the Hartley or Weaver architectures must incorporate calibration, i.e., a method of cancelling the gain and phase mismatches. A number of calibration techniques have been reported so far in many literatures.

For example, the Self-Calibrating Architecture introduced by Montemayor and Razavi, determines the phase and gain mismatches of a Weaver architecture, and drives their magnitudes towards zero through use of a negative feedback loop. Other calibration methods include Sign-Sign Least Mean Square (SS-LMS) calibration, Variable Delay Cell, Variable Gain Cell etc.

Conclusion

The demand for fully monolithic wireless receivers has fuelled the development of new image-reject architectures that eliminate the need for explicit, off-chip filters. It also proves to be a low power solution to image rejection. However, the accuracy of the image-reject receivers is of great concern as they are susceptible to mismatches. The technologists have come up with various calibration techniques that sufficiently improve the IRR.

References

[1] RF Microelectronics, Behzad Razavi, 2nd edition, Prentice Hall, 2012

[2] B. Razavi, “Architectures and Circuits for RF CMOS Receivers,” IEEE Custom Integrated Circuits Conference, pp. 393-400, 1998.

[3] J. Chow, K. Phang, “RF IMAGE-REJECT RECEIVERS”, 2002

Questions?

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