1. Distortion in Nonlinear SystemsGain Compression.Harmonic DistortionIntermodulation DistortionCross ModulationSecond Order NonlinearityMeasuring Intermodulation DistortionSet the amplitude of generators at f1 and f2 to be equal.Start at a very low input power using the variable attenuator, then increase power in steps until you begin to see the IMD output on the spectrum analyzer. The resolution bandwidth should be narrow so that the noise floor is reduced. This will allow visibility of the IMD signal at lower power levels.Plot the IMD power vs. input power and verify that the slope is close to 3. Then, you can calculate the IIP3 as described previously.Two tone simulation in ADSHow is the Third-Order Intercept Point affected by cascaded stages?Example: Third-order intercept of a receiver front end2. Next Topic: NOISEID = diode currentNoise Equivalent BandwidthSignal-to-noise ratioSecond Stage Noise ContributionECE145A/ECE218A Performance Limitations of Amplifiers 1. Distortion in Nonlinear Systems The upper limit of useful operation is limited by distortion. All analog systems and components of systems (amplifiers and mixers for example) become nonlinear when driven at large signal levels. The nonlinearity distorts the desired signal. This distortion exhibits itself in several ways: 1. Gain compression or expansion (sometimes called AM – AM distortion) 2. Phase distortion (sometimes called AM – PM distortion) 3. Unwanted frequencies (spurious outputs or spurs) in the output spectrum. For a single input, this appears at harmonic frequencies, creating harmonic distortion or HD. With multiple input signals, in-band distortion is created, called intermodulation distortion or IMD. When these spurs interfere with the desired signal, the S/N ratio or SINAD (Signal to noise plus distortion ratio) is degraded. Gain Compression. The nonlinear transfer characteristic of the component shows up in the grossest sense when the gain is no longer constant with input power. That is, if Pout is no longer linearly related to Pin, then the device is clearly nonlinear and distortion can be expected. Pout Pin P1dB, the input power required to compress the gain by 1 dB, is often used as a simple to measure index of gain compression. An amplifier with 1 dB of gain compression will generate severe distortion. Distortion generation in amplifiers can be understood by modeling the amplifier’s transfer characteristic with a simple power series function: 313out in inVaVaV=− Of course, in a real amplifier, there may be terms of all orders present, but this simple cubic nonlinearity is easy to visualize. The coefficient a1 represents the linear gain; a3 the 1 rev. 12/29/10 © 2010 Prof. S. LongECE145A/ECE218A Performance Limitations of Amplifiers distortion. When the input is small, the cubic term can be very small. At high input levels, much nonlinearity is present. This leads to gain compression among other undesirable things. Suppose an input Vin =A sin (ωt) is applied to the input. 2331331sin( ) sin(3 )44outaAVAa t aA tωω⎡⎤=− +⎢⎥⎣⎦ Gain Compression Third Order Distortion Gain compression is a useful index of distortion generation. It is specified in terms of an input power level (or peak voltage) at which the small signal conversion gain drops off by 1 dB. The example above assumes that a simple cubic function represents the nonlinearity of the signal path. When we substitute Vin(t) = A sin (ωt) and use trig identities, we see a term that will produce gain compression: A(a1 - 3a3A2/4). If we knew the coefficient a3, we could predict the 1 dB compression input voltage. Typically, we obtain this by measurement of gain vs. input voltage. Harmonic Distortion We also see a cubic term that represents the third-order harmonic distortion (HD) that also is caused by the nonlinearity of the signal path. Harmonic distortion is easily removed by filtering; it is the intermodulation distortion that results from multiple signals that is far more troublesome to deal with. Note that in this simple example, the fundamental is proportional to A whereas the third-order HD is proportional to A3. Thus, if Pout vs. Pin were plotted on a dBm scale, the HD power will increase at 3 times the rate that the fundamental power increases with input power. This is often referred to as being “well behaved”, although given the choice, we could easily live without this kind of behavior! 2 rev. 12/29/10 © 2010 Prof. S. LongECE145A/ECE218A Performance Limitations of Amplifiers Intermodulation Distortion Let’s consider again the simple cubic nonlinearity a3vin3. When two inputs at ω1 and ω2 are applied simultaneously to the RF input of the system, the cubing produces many terms, some at the harmonics and some at the IMD frequency pairs. The trig identities show us the origin of these nonidealities. [4] We will be mainly concerned with the third-order IMD. (actually, any distortion terms can create in-band signals – we will discuss this later). IMD is especially troublesome since it can occur at frequencies within the signal bandwidth. For example, suppose we have 2 input frequencies at 899.990 and 900.010 MHz. Third order products at 2f1 - f2 and 2f2 - f1 will be generated at 899.980 and 900.020 MHz. These IM products may fall within the filter bandwidth of the system and thus cause interference to a desired signal. The spectrum would look like this, where you can see both third and fifth order IM. 3 rev. 12/29/10 © 2010 Prof. S. LongECE145A/ECE218A Performance Limitations of Amplifiers P1IIP3Pin (dBm)fundamentalthird-order IMDPIMDPout (dBm)POIP3INx2xP1IIP3Pin (dBm)fundamentalthird-order IMDPIMDPout (dBm)POIP3INx2xx = IIP3 - PIN ()1312INIMD IMD power, just as HD power, will have a slope of 3 on a Pout vs Pin (dBm) plot. A widely-used figure of merit for IMD is the third-order intercept (TOI) point. This is fictitious signal level at which the fundamental and third-order product terms wouldintersect. In reality, the intercept power is 10 to 15 dBm higher than the P1dB gain compression power, so the circuit does not amplify or operate correctly at the IIP3level. The higher the TOI, the better the large signal capability of the system. If specified in terms of input power, the intercept is called IIP3. Or, at the output, OIP3. This power level can’t be actually