TELECOMMUNICATIONS Dr. Hugh Blanton ENTC 4307/ENTC 5307

Thermal Noise Definition

Dr. Blanton - ENTC Introduction 3 / 30 All dissipative (resistive) elements generate thermal, or Johnson, noise. This noise power is expressed in Watts as P N = kTB (note: P N is not a function of resistance) where k — (Boltzman constant) 1.38  joule/K T — the temperature in Kelvin B — the bandwidth used to measure the noise power, expressed in Hz

Dr. Blanton - ENTC Introduction 4 / 30 At room temperature (T o = 294K) the thermal noise generated in a 1 Hz bandwidth, B o : P N = kTB = ( 1.38  )(294)(1) =  W =  mW = -174 dBm

Dr. Blanton - ENTC Introduction 5 / 30 In an ideal noiseless system, the thermal noise controls the lowest detectable signal. In a true physical system, the noise of the system is added to the thermal noise to establish the “Noise Floor.” Generally the minimum useful signal level is well above the Noise Floor.

Dr. Blanton - ENTC Introduction 6 / 30 Noise Floor Definition The dB difference between the KTB thermal noise power and the actual noise power is called Noise Figure (NF). When it is referenced to the input port of a circuit or system, the Noise Figure:

Dr. Blanton - ENTC Introduction 7 / 30 The term “Noise Floor” in a linear noisy system is computed for various bandwidths as:

Dr. Blanton - ENTC Introduction 8 / 30 In an actual physical system, in the absence of IM distortion, the Noise Figure at the input determines the lowest detectable signal. However, for error-free detection, a certain minimum “signal-to-noise ratio” is required.

Dr. Blanton - ENTC Introduction 9 / 30 Harmonic distortion in amplifiers is caused by nonlinear effects on the sinusoidal waveform. Distortion components are created at integer multiples of the signal frequency shown below:

Dr. Blanton - ENTC Introduction 10 / 30

Dr. Blanton - ENTC Introduction 11 / 30 A memoryless nonlinearity may be described by a Power Series where the real coefficients of some of the terms may have negative signs. If the input signal is a sinusoidal wave, the higher order terms at the output show up in forms of higher frequencies, harmonically related to VIN.

Dr. Blanton - ENTC Introduction 12 / 30

Dr. Blanton - ENTC Introduction 13 / 30 Output/Input dB power plots of the fundamental signal, 2 nd, and 3rd harmonics indicate that their slopes are different. Slopes: Fundamental signal, 1:1 2nd harmonics, 2:1 3rd harmonics, 3:1 Harmonic distortion adds a DC offset due to RF detection. The fundamental signal output is changed due to compression. Additional frequencies are created, having P IN /P OUT slopes greater than unity.

Dr. Blanton - ENTC Introduction 14 / 30 Gain Compression If the magnitude of the input signal (A) is raised to a sufficient level, the gain term of the fundamental output will compress, due to the fact that the sign of a 3 is negative. The power level where the actual fundamental output power is 1 dB less than expected, is called the 1dB Gain Compression, or P 1dB of the amplifier.

Dr. Blanton - ENTC Introduction 15 / 30 In hard compression, beyond P 1dB, the higher order terms become more dominant and the output waveform begins to look like a square- wave.

Dr. Blanton - ENTC Introduction 16 / 30 The theoretical output level where third order distortion products (2F1-F2) & (2F2-F1) equal the desired output signal level is called the third order output intercept, OIP3.

Dr. Blanton - ENTC Introduction 17 / 30 Referred to the input this level is IIP3. The 1dB compression level is ABOUT 10dB below OIP3. In exceptional devices, 20dB.