Communication Systems. Department of Electronics and Electrical Engineering

Transcription

1 COMM 704: Communication Lecture 6: Oscillators (Continued) Dr Mohamed Abd El Ghany Dr. Mohamed Abd El Ghany,

2 Course Outline Introduction Multipliers Filters Oscillators Power amplifiers AM/FM modulation Transceiver architectures Television Satellite communications systems

3 Wien-Bridge Oscillators AWienbridge Wien-bridge oscillator uses a noninverting amplifier and RC phaseshifting network. The oscillation frequency w o is inversely proportional to RC product of the feedback network. For an oscillator, Aβ= f o = πrc R f R = Assume: R =R 3 =R C =C =C 3

4 LC Oscillators LC oscillators have the advantage of having relatively small reactive elements. They exhibit higher Q than RC oscillators, but they are difficult to tune over a wide range. LC Oscillators Colpitts Oscillators Hartley Oscillators 4

5 Colpitts Oscillators For an oscillator, Aβ= C + w osc = L C C C R = R C C 3 5

6 Hartley Oscillators For an oscillator, Aβ= w R L = = osc C ( L + ) R L ( L 3 6

7 Crystal Oscillators Because of their excellent frequency stability, quartz crystals are commonly used to control the frequency of oscillation. If the inductor L of the Colpitts oscillator is changed to a crystal, the oscillator is called a crystal oscillators. Crystal oscillators are commonly used in digital signal processing. Crystal reactance Inductive Capacitive 7

8 Crystal Oscillators Properties of the crystal: The quality factor Q of the crystal can be as high as several hundred thousand. L has a large value (as high as hundreds of henries) R s can be as high as a few hundred thousand ohms. C p >> C s, C p (parallel capacitance) of order of pf. 8

9 Crystal Oscillators Since Q is very high in the typical quartz crystal, we may neglect Rs. The crystal impedance is given by: z ( s) = ( sl + ) //( sc s sc p ) z( s) = ( sc p )( s s + LC s + C + C s L( C s C p p ) ) w s = LC s w w s z( jw ) = ( j )( wc w w p p ) w p = C s C s + C C p p L 9

10 Colipitts Oscillator Using a Crystal w osc = + ( C + C ) + s p C C LC s + C + p C C C p >> C s w osc = LC s 0

11 Ring Oscillators Odd Number of Inversions If a cascade of M gain stages with an odd number of inversions is placed in a feedback loop, the circuit oscillates with a period equal to MT d, where T d is the delay of each stage. The oscillation can be viewed as occurring at the frequency for which the total phase shift is zero and the loop gain is unity.

12 Ring Oscillators Example: Differential Ring Oscillator A differential ring oscillator is shown. a) Find the frequency of oscillation in Hz if R=KΩ and C= pf b) What value of g m is required for oscillation assuming all stages are identical? c) What is the maximum positive and maximum negative voltage swing at the drains if I ss = ma and V DD =V?

13 Ring Oscillators Example: continued Solution a) The voltage transfer function of a single stage is, V ( s) g R g R out m m = = where τ = RC = 0 9 sec s V ( s) src + sτ in + The phase shift around the loop will be 360 o or 0 o. Therefore, the oscillation frequency can be found as, 3 tan ( w τ ) = π osc.73 f osc = = π RC MHz 3

14 Ring Oscillators Example: continued Solution b) The magnitude of the loop gain at the oscillation frequency is given as g R ( w ) + RC 3 m = R = +.73 = + 3 = osc g m g m = = ms R c) V max = V DD = V and v min = V DD -I ss R= - = V v = V max v = V min 4

15 Phase Noise As other analog circuits, oscillators are susceptible to noise. Noise injected into an oscillator by its constituent devices or by external means may influence both the frequency and the amplitude of the output signal. In most cases, the disturbance in the amplitude is negligible, and only the random deviation of the frequency is considered. In RF application, phase noise is usually characterized in the frequency domain. for an ideal sinusoidal oscillator operating at w c, the spectrum assumes the shape of an impulse, whereas for an actual oscillator, the septum exhibits skirts around the carrier frequency. Ideal Oscillator Actual Oscillator 5

16 Phase Noise To quantify phase noise, we consider a unit bandwidth at an offset w with respect to w c, calculate the noise power in this bandwidth, and divide the results by the carrier power. 6

17 Phase Noise Effect of phase noise in RF Communications The carrier signal for the receiver path The carrier signal for the transmit path If the Local Oscillator (LO) output contains phase noise, both downconverted and upconverted signals are corrupted. 7

18 Phase Noise Effect of phase noise in RF Communications : (continued ) Down conversion by an ideal oscillator The signal of interest is convolved with an impulse and thus translated to a lower (and a higher) frequency with no change in the shape 8

19 Phase Noise Effect of phase noise in RF Communications : (continued ) Reciprocal mixing In reality, the wanted signal may be accompanied by a large interferer in an adjacent channel, and the local oscillator exhibits finite phase noise. When the two signal are mixed with the LO output, the downconverted band consists of two overlapping spectra, with the wanted signal suffering from significant noise due to the tail of the interferer. This effect is called reciprocal mixing 9

20 Phase Noise Effect of phase noise in RF Communications : (continued ) Effect of phase noise in transmitters Suppose a noiseless receiver is to detect t a weak signal at w while a powerful, nearby transmitter generates a signal at w with substantial phase noise. Then, the wanted signal is corrupted by the phase noise tail of the transmitter. 0

21 Phase Noise Effect of phase noise in RF Communications : (continued ) Example: in the figure, where the wanted channel is 30 KHz wide and 60 db below an unwanted channel 60 KHz away. How low should the phase noise of the unwanted channel 60 KHz offset be so that the SNR in the desired channel exceeds 5 db? Solution The total noise power introduced by the interferer in the desired channel is equal to p f H = S ( f df Where S n (f) denotes the phase noise profile of the unwanted ) n, tot f n L channel and f L and f H are the lower and upper ends of the desired channel, respectively. For simplicity, we assume s n (f) is constant in this bandwidth and equal to S = tt o, p S ( f f ) n, tot o H L

22 Phase Noise Effect of phase noise in RF Communications : (continued ) Solution: (continued) SNR = S P sig ( f f o H L ) 0 log( S / P ) = 5 db 0 log( f f ) o sig H L 0 log P 0 log P = 60 db int sig P int is the interferer power 0 log( S / P ) = 5 db 0 log( f f ) 60 db o int H L The phase noise must not exceed -0dBc/Hz at 60 khz offset. When integrated in a 30 KHz band, the phase noise must not exceed -70 dbc

23 Q of an Oscillator The definition of Q that proves especially useful in oscillators is shown in the following figure The Q is defined as w dφ o Q = dw Where φ ( w ) is the phase of the openloop transfer function 3