AN0001

AN0001 RFMD | Alldatasheet

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Copyright 1997-2002 RF Micro Devices, Inc. such as BPSK, QAM, and QPSK. a derivation showing the relationship between these four parameters. fore, the need to optimize the carrier suppression and the sideband suppression of a quadrature modulator often arises. this optimization easier to understand and perform. error and phase error are related. The block diagram of a typical quadrature modulator is shown in Figure 1. local oscillator. These signals are then summed to form the RF output signal. Figure 1. Quadrature Modulator Functional Block Diagram

Copyright 1997-2002 RF Micro Devices, Inc. Derivation To begin the derivation, the input signals are defined as follows: Note that this implies that the error injected into the system is due to the in-phase signal. The amplitude G represents the ratio of the amplitudes of the input signals. The phase offset, φ, represents the phase error. This is typically a small value representing how far from quadrature the signals are. The DC offset, D, represents the DC offset between the two sig- nals. Ideally there is no offset, but in practice, there is an offset introduced by imbalances in the modulator circuitry. The quadrature signal is, by definition, 90° out of phase with the in-phase signal. With the signals defined, it is a matter of performing the mathematical analysis that parallels the modulators’ functional- ity. The RF output is given by As can be seen, the carrier can only be present at the output if there is a DC offset between the input signals. Now, rear- range the terms to get the upper sideband and lower sideband terms using the trigonometric identities These can be rewritten to obtain Applying the trigonometric identity1 with the final form of the equations is reached It() G ω t φ+() D+cos= Qt() ω t 90°+()cos= RF t() G ω t φ+()cos ω ct() D ω ct() ω ct()sin–cos+ ω t 90°+()coscos= α()sin β() 1 2--- αβ–() 1 2---+sin αβ+()sin=cos α()cos β()cos 1 2---= αβ–() 1 2---+cos αβ+()cos USB t() 1 2---G ω ct ω t φ++()cos 1 2---– ω ct ω t 90°++()sin= LSB t() 1 2---G ω– ct ω t φ++()cos 1 2---– ω ct ω t–9 0 °–()sin= USB t() 1 2---G ω ct ω t φ++()cos 1 2---– ω ct ω t+()cos= LSB t() 1 2---G ω t ω ct φ+–() 1 2---+cos ω ct ω t–()cos= αβ+()cos α()cos β()cos α() β ()sinsin–= αω ct ω t+= βφ= USB t() 1 2---G ω ct ω t+()cos φ() 1 2---–cos G ω ct ω t+()sin φ() 1 2---–sin ω ct ω t+()cos= LSB t() 1 2---G ω t ω ct–()cos φ()cos 1 2---– G ω t ω ct–()sin φ() 1 2---+sin ω ct ω t–()cos=

Copyright 1997-2002 RF Micro Devices, Inc. We want these equations in this form is to allow them to be easily converted to envelope-phase form2 since the sideband suppression is the ratio of the magnitude (envelope) of the upper sideband to the magnitude of the lower sideband. In general, a signal can be represented as the sum of the real and imaginary terms This expression can be rewritten in envelope-phase form as follows where The upper sideband and lower sideband envelopes are After expanding these terms we obtain The ratio for sideband suppression is then given by Therefore, the lower sideband suppression in dBc (decibels relative to the upper sideband) is given by This expression can be plotted as a set of suppression contours, 3 with amplitude error and phase error as the axes. To facilitate this, the equation was solved for phase error, φ, in terms of amplitude error, G, and sideband suppression, SBS. xt() xR t() ω t() xI t() ω t()sin–cos= xt() rt() ω t φ t()+[]cos= rt() xR t() xI–2 t()2= φ t() xI t() USB env 2---G φcos 1 2---–  2 1 2---– G φsin  2 LSB env 2---G φcos 1 2---+  2 1 2---– G φsin  2 USB env 4---G2 1 2---G φcos 1 4---+–= LSB env 4---G2 1 2---G φcos 1 4---++= USB env LSB env 4---G2 1 2---G φcos 1 4---+– 4---G2 1 2---G φcos 1 4---++ G2 2G φcos 1++ Suppression dBc() 20 G2 2G φcos 1+– G2 2G φcos 1++ G2 2G φcos 1++ φ 11 0 SBS G210 SBS G2+–– 2G10 SBS 2G+

Copyright 1997-2002 RF Micro Devices, Inc. program. This data was plotted and the result is contained in Figure 2. assuming the amplitude error has been balanced. Figure 3 is such a plot. Figure 2. Sideband Suppression vs. Amplitude Error and Phase Error

Copyright 1997-2002 RF Micro Devices, Inc. Carrier suppression is a function of the DC offset between the in-phase signal and the quadrature signal in the device. This offset can be compensated by altering the DC offset of the input signals. Therefore, to improve the carrier suppres- sion, start by adjusting the DC component of the in-phase signal (which should nominally be equal to V REF), watching the output on the spectrum analyzer. As it is adjusted, there will be a point where the carrier level is minimized. Next, do the same with the DC component of the quadrature signal. Again, there will be a point where the carrier level is mini- mized. At this point, the carrier suppression has been optimized. The change to each DC level should be no more than about 20mV. The carrier suppression can also be adjusted by adjusting V REF. This is a course adjustment since VREF is connected to both IREF and QREF and the degrees of freedom have been reduced. The above procedure could then be used to fine tune the adjustment. Either way, the same results should be obtained. Sideband suppression is a function of both the amplitude error and the phase error of the device. These errors can be compensated by adjusting the input signals. Therefore, to optimize the sideband suppression, begin by adjusting the amplitude of the in-phase signal . There will be a point when th e sideband level is at a mini mum. Next, do the same for the quadrature signal. Again, t here will be a point when the sideband level is minimized. To optimize further, adjust the phase of the quadrature signal. Again, there will be a point where the sideband level is minimized. At this point, the side- band suppression is optimized. The change in the amplitude should be no more than about 10mV and the change in phase should be no more than about 4°. Table 1 provides a list of the test equipment used. Conclusions This note has presented the derivation of the relationship that exists between the four primary specifications for a quadrature modulator: carrier suppression, sideband suppression, phase error, and amplitude error. Equations were pre- sented that allow for translation between sideband suppression and phase and amplitude error. These equations were used to generate a plot that allows the designer of a syste m to quickly see how these specifications interact. It can be seen that good sideband suppression is the combination of both little phase error and little amplitude error. It is often desirable to optimize the carrier suppression and the sideband suppression of quadrature modulators. This article presented a simple and straight-forward method of pe rforming this optimization. This method is suitable for other similar devices and has been used to increase their performance. An example of the outlined optimization method was used to improve the performance of an RF2422. For an RF2422 evaluation board, a carrier suppression of 44.1dB and a sideband suppression of 54.5dB were achieved. This is roughly a 15dB to 20dB improvement over an uncompensated board. Comparable improvements have been attained with other quadrature modulators. References 1. M. Spiegel, Mathematic al Handbook of Formulas and Tables, McGraw-Hill Book Company, 1968. 2. R. E. Ziemer, Introduction to Digital Communication, Macmillan Publishing Company, 1992. 3. W. Djen, Application Note AN1892, Philips Semiconductors, December 1994. Signal Equipment Local Oscillator Rohde&Schwarz SMT -03 Signal Generator V CC and VREF Hewlett-Packard E3620A Dual Output Power Supply I and Q Signals Hewlett-Packard 8904A 4-Channel Multifunction Synthesizer RF Output Hewlett-Packard 8593E Spectrum Analyzer