# TSEK03: Radio Frequency Integrated Circuits (RFIC)

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1 TSEK03: Radio Frequency Integrated Circuits (RFIC) Lecture 6: Mixers (cont) Ted Johansson, EKS, ISY

2 Overview 2 Razavi: Chapter , pp Lee: Chapter Mixers general 6.2 Passive downconversion mixers 6.3 Active downconversion mixers

3 6.3 Active Mixers 3 Active mixers perform three functions: (1) they convert the RF voltage to a current, (2) commutate (steer) the RF current by the LO, (3) convert the IF current to voltage.

4 Double-Balanced Active Mixers 4 For differential inputs, we can create a double-balanced active mixer.

5 Conversion Gain 5 With abrupt LO switching, the circuit reduces to that shown in figure below (left)

6 Conversion Gain 6 We have for R1 = R2 = RD Square-wave toggle with fundamental amplitude equal to 4/π

7 Active Mixer with LO at CM Level Low supply voltage limits the gain of active mixers

8 Example A single-balanced active mixer requires an overdrive voltage of 300 mv for the input V/I converter transistor. If each switching transistor has an equilibrium overdrive of 150 mv and the peak LO swing is 300 mv, how much conversion gain can be obtained with a 1 V supply? Eq 6.44: VR,max = 444 mv and hence Relatively low conversion gain => the noise contributed by the load resistors and following stages may become significant. RFIC Ted Johansson

9 Conversion Gain 9 The conversion gain may also fall if the LO swing is lowered. While M 2 and M 3 are near equilibrium, the RF current produced by M 1 is split approximately equally between them, thus appearing as a common-mode current and yielding little conversion gain for that period of time. Reduction of the LO swing tends to increase this time and lower the gain.

10 Example The figure shows a dual-gate mixer, where M1 and M2 can be viewed as one transistor with two gates. Identify the drawbacks of this circuit.

11 Example For M2 to operate as a switch, its gate voltage must fall to VTH2 above zero regardless of the overdrive voltages of the two transistors. For this reason, the dual-gate mixer typically calls for larger LO swings than the single-balanced active topology does. Furthermore, since the RF current of M1 is now multiplied by a square wave toggling between 0 and 1, the conversion gain is half:

12 Example Additionally, all of the frequency components produced by M1 appear at the output without translation because they are multiplied by the average value of the square wave = 1/2. Thus, half of the flicker noise of M1 a highfrequency device and hence small emerges at IF. Also, low-frequency beat components resulting from even-order distortion in M1 directly corrupt the output, leading to a low IP2. The dual-gate mixer does not require differential LO waveforms, a minor advantage. For these reasons, this topology is rarely used in modern RF design.

13 Effect of Gradual LO Transitions 13 With a sinusoidal LO, the drain currents remain approximately equal for a fraction of each half cycle, ΔT. The circuit exhibits little conversion gain during these periods.

14 Example Repeat Example 6.12 but take the gradual LO edges into account. A single-balanced active mixer requires an overdrive voltage of 300 mv for the input V/I converter transistor. If each switching transistor has an equilibrium overdrive of 150 mv and the peak LO swing is 300 mv, how much conversion gain can be obtained with a 1 V supply? The gain in the Example 6.12 must be multiplied by ( ) ~ 0.97 => gain is now 11.3 db, 0.2 db lower.

15 Effect of capacitance With abrupt LO edges, M2 is on and M3 is off, yielding a total capacitance at node P equal to: 15 The RF current produced by M1 is split between CP and the resistance seen at the source of M2, 1/gm2. The voltage conversion gain is modified as:

16 Example Compare the voltage conversion gains of single-balanced and double-balanced active mixers.

17 Example From previous discussion, we know that (VX1 - VY1)/VRF+ is equal to the voltage conversion gain of a singlebalanced mixer. Also, VX1 = VY2 and VY1 = VX2 if VRF- = -VRF+. Thus, if Y2 is shorted to X1, and X2 to Y1, these node voltages remain unchanged. The differential voltage conversion gain of the double-balanced topology is therefore given by:

18 Example This gain is half of that of the single-balanced counterpart. This reduction arises because the limited voltage headroom disallows a load resistance of RD.

19 6.3.2 Noise in Active Mixers 19 The noise components of interest lie in the RF range before downconversion and in the IF range after downconversion. The frequency translation of RF noise by the switching devices prohibits the direct use of small-signal ac and noise analysis in circuit simulators, necessitating simulations in the time domain. Moreover, the noise contributed by the switching devices exhibits time-varying statistics,

20 Quantitative Analysis 20 To estimate the input-referred noise voltage, we apply the following procedure: 1. for each source of noise, determine a conversion gain to the IF output. 2. multiply the magnitude of each noise by the corresponding gain and add up all of the resulting powers, thus obtaining the total noise at the IF output. 3. divide the output noise by the overall conversion gain of the mixer to refer it to the input.

21 Example Study the effect of LO noise on the performance of double-balanced active mixers.

22 Example Drawing the circuit as shown below, we note that the LO noise voltage is converted to current by each switching pair and summed with opposite polarities. Thus, the double-balanced topology is much more immune to LO noise a useful property obtained at the cost of the 3-dB noise and the higher power dissipation.

23 6.3.3 Linearity 23 The input transistor imposes a direct trade-off between nonlinearity and noise: The linearity of active mixers degrades if the switching transistors enter the triode region. Thus, the LO swings cannot be arbitrarily large.

24 Example An active mixer exhibits a voltage conversion gain of 10 db and an input 1-dB compression point of 355 mvpp (= -5 dbm). Is it possible that the switching devices contribute compression? At an input level of -5 dbm, the mixer gain drops to 9 db, leading to an output differential swing of 355 mvpp Vpp. Thus, each output node experiences a peak swing of 250 mv (node X falls 250 mv below its bias point). If the LO drive is large enough, the switching devices enter the triode region and compress the gain.

25 Using Nonlinearity for Mixing 25 A nonlinear system can be used as mixer. We can describe the input-output relationship of a nonlinear system by polynomial expansion as: Considering v in as sum of the RF input and LO signal, the output of this system includes a DC term and harmonics of the inputs and IM products as pω RF ± qω LO Normally, p = q = 1 is desired. To avoid higher-order nonlinearities, we can use a square-law mixer.

26 Square-Law Mixer 26 For a square-law mixer only c 1 and c 2 are non-zero (c 0 is a DC term which can be removed by filtering). Input signal: the sum of RF and LO signals Output signal has three components:

27 Square-Law Mixer 27 The useful term is v cross and can be rewritten as: If LO amplitude is fixed, IF output is proportional to the RF input amplitude. We have our mixer! Since the current in long-channel MOSFET devices has a quadratic form, they are good candidates for square-law mixers.

28 Square-Law Mixer 28 Since the current in long-channel MOSFET devices has a quadratic form, they are good candidates for squarelaw mixers. Sum of RF and LO signals are applied to the gate. It is not good because of poor isolation between these signals. Conversion gain:

29 Square-Law Mixer 29 To reduce the interaction between RF and LO ports, we can apply LO signal to the source. Conversion gain: Independent of bias, but LO amplitude, temperature.

30 Summary 30 Mixers are used for frequency conversion. Popular radio architecture that need mixing are heterodyne and direct-conversion TRX. Any non-linear device can be used for mixing. Square-law mixers use the non-linearity behavior of (often) a single device, a transistor or diode. Commonly, mixers are of multiplier type and have three ports: RF, IF, and LO. Mixers can be passive or active.

31 Active or passive mixer? 31 According to Li (*), passive mixers are useful at microwave frequencies, active at lower frequencies. (*) R. C.-H. Li, "RF Circuit Design", p. 78, Wiley 2009.

32

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