E4215: Analog Filter Synthesis and Design: HW0

Transcription

1 E425: Analog Filter Synthesis and Design: HW0 due on 2 Jan This assignment has ZEO credit and does not contribute to the final grade. Its purpose is to gauge your familiarity of prerequisite topics.. heck the terms that are unfamiliar to you: Laplace transform Impulse response Frequency response Transfer function Bode plot Operational amplifier Bipolar transistor MOS transistor Small signal equivalent circuit ommon drain amplifier Loop gain Gain margin Phase margin 2. The circuit in Fig. is v o v i = 3. The circuit in Fig. 2 is I c = v i Figure : ma x Figure 2: 5. The circuit in Fig. 4 is 6. The circuit in Fig. 5 is V x = V y = L v o x I c 4. The circuit in Fig. 3 is v o v i = 7. Transfer function of the circuit in Fig. 6: (s) (s) =

2 2 KΩ KΩ 2KΩ v v2 V KΩ V x ideal opamp V y 2mA Figure 5: Figure 3: v i v o Figure 6: Figure 4: 3Vcos(ωt) KΩ 2KΩ 8. In Fig. 7 Figure 7: = L 9. Transfer function of the circuit in Fig. 8: (s) (s) = 0. In Fig. 9: Figure 8: v o v i = g m r ds L v i v o Figure 9:

3 E425: Analog Filter Synthesis and Design: HW due on 28 Jan (s) i i (t) (s) (s) i i (t) /2 2 (s) (s) v x v x 2 2 (s) v i (t)=vcos(t/) (c) v o (t) i(t) v i (t)=vcos(t/) v(t) (e) /2 2 (d) v o (t) (s) /4 v x v x (s) Figure : v i (t) V. (5 pts.) For the circuits in Fig. and Fig., evaluate the transfer function H(s) = (s)/ (s), and the impulse response h(t) corresponding to H(s). Approximately sketch the magnitude and phase of H(s) (Bode Plot). What is the difference between the two circuits? 2. (5 pts.) In the circuits in Fig. (c) and Fig. (d), evaluate the current i i (t) through the input voltage source. Evaluate the average power dissipated in the voltage source and the resistor. What is the difference between the two circuits? Note: Average power dissipated in an element with a voltage v(t) across it and a current i(t) through it (see Fig. (e)) is given by P = T T 0 v(t)i(t)dt 3. (5 pts.) Write the expressions for the transfer function H(s) = (s)/ (s) for the circuits in 0V T (c) Figure 2: Fig. 2 and Fig. 2. Sketch the Bode plots assuming = (5 pts.) The circuit in Fig. 2 is driven by a pulse with an amplitude V and lasting T seconds (Fig. 2(c)). Assuming T =, sketch the intermediate voltage v x (t). Sketch the output voltage v o (t) assuming that 2 2 =.

4 E425: Analog Filter Synthesis and Design: HW2 due on 4 Feb For the opamps, use the appropriate model based on the parameters provided. i.e. if nothing is given, assume an ideal opamp with infinite gain; if the unity gain frequency is given, use the integrator model; if the dc gain and the unity gain frequency are given, use the first order model etc. This holds for all future assignments. unity gain frequency ω u = Grad/s, draw the Bode plot (magnitude and phase) of loop gain T (s) and op amp gain A(s). 4. (6 pts.) Assume g m = ms, = 900 kω, 2 = 00 kω, L =, A o = 000. For the circuits in Fig. 2 and Fig. 2, evaluate the gain / and the feedback loop gain T. epeat, assuming L = MΩ (6 pts.) Assume g m = ms, = 900 kω, 2 = 00 kω, L = 0 pf, A o = v i?? v o v g m v o 000, ω u = 00 Mrad/s 2. For the circuits in Fig. 2(c) and Fig. 2(d), evaluate the transfer function (s)/ (s) and the feedback loop gain T(s). Write the transfer functions in the standard first order form and compare the two Figure : results. epeat, assuming L = 20 pf.. (2 pts.) [Fig., g m = 4/] Assign the correct signs to the opamp such that it has negative feedback at dc. 2. (2 pts.) [Fig., g m = 4/] Assuming that the opamp has a transfer function A(s) = ω u /s, determine the transfer functions (s)/ (s), V (s)/ (s). 3. (4 pts.) [Fig., g m = 4/] Determine the loop gain T (s) around this feedback loop. Assuming that the opamp has a dc gain A o = 00 and a giga radians/second; giga=0 9 2 mega radians/second

5 2 g m = ms A o = L 2 L g m = ms A o = 000, ω u = 00Mrad/s 2 2 L L (c) (d) Figure 2:

6 E425: Analog Filter Synthesis and Design: HW3 due on Feb In addition to the problems here, problems, 2, 3 from HW2 are also due on Feb Vin Vin Vin2 kω kω kω kω kω kω kω opamp with offset kω opamp with offset kω opamp with offset Figure : Vo Vo Vo2 kω kω Vo. (9 pts.) The opamps in Fig. have an input referred offset voltage s, but are otherwise ideal (A 0 = ). For Fig., derive the expression relating the output to the input n and the offset s. Draw the dc transfer characteristics vs. n including the effect of offset assuming that s > 0. Show the input referred offset and the output offset of the amplifier in Fig. on this plot. (Hint: In a circuit with multiple inputs, try using superposition). If the standard deviation of s is σ = 5 mv, what is the standard deviation of the input referred offset and the output offset of the amplifier in Fig.. What is the net output offset (in the output ) of the circuit in Fig.? (Hint: Use the results related to Fig. to determine and 2. elate to and 2 ) 2. (5 pts.) In Fig. 2, determine V p,max, the maximum value of V p such that the output v o (t) is sinusoidal. The opamp has the characteristic shown in Fig. 2 (The slope of the vertical part is. Sketch v o (t) when V p = V p,max /2 and when V p = 2V p,max 3. (3 pts.) In Fig. 3, v o = f(v i ) = v i a 2 v 2 i a 3 v 3 i. If v i = V p cos(ωt), express v o (t) as a sum of sinusoids. Find the ratio of the 2 nd and 3 rd harmonic amplitudes to that of the fundamental. If a 2 = 0 3 V, a 3 = 0 3 V 2, find the input peak V p such that the second harmonic is 60 db below the fundamental. epeat the exer

7 2 2kΩ kω v in =V p cos(ωt) v o V v out g m2 V v id g m Figure 2: v i f(v o ) v o g m3 g m2 Figure 3: cise for the third harmonic. 2 g m 4. (3 pts.) Assuming ideal transconductors, derive expressions relating to in Fig. 4 and to and 2 in Fig. 4. epeat for Fig. 4 assuming that the transconductor g mx has an output resistance r ox and input and output capacitances ix, ox. x = {, 2} for the two transconductors in Fig. 4. Figure 4: voltage controlled current source

8 E425: Analog Filter Synthesis and Design: HW4 due on 8 Feb S the transfer function to the original? eevaluate v s (t) firstorder filter L v o (t) the transfer function with S = 0, L = MΩ. How would you restore the pole to the original value? Figure :. Initially, assume S = 0, L =. Fig. shows a first order filter whose input is the sum of two sinusoids v s (t) = V cos( Mrad/s t) V cos(000 Mrad/s t). The higher frequency sinusoid should be attenuated by 40 db and the lower frequency sinusoid should be attenuated as little as possible. v s (t) ( pt.) With S = 0 kω, L = MΩ, choose, such that the pole of the filter is the same as originally determined. What is the transfer function? Determine the attenuation of the two sinusoids. 2 N v o (t) (2 pts.) Determine the transfer function of the filter. Draw the schematic of a passive filter with = 00 kω that will accomplish this. What is the attenuation (in db) of the lower frequency sinusoid? (3 pts.) In the previously designed filter, if and can have variations of ±0%, What are the maximum and minimum values of the pole frequency? What is the percentage variation from the nominal value? What is the worst case (smallest) attenuation of the higher frequency signal? (c) What is the worst case (largest) attenuation of the lower frequency signal? ( pt.) eevaluate the transfer function with S = 0 kω, L =. How would you restore Figure 2: 2. (3 pts.) Fig. 2 shows a cascade of N identical buffered first order filter sections. v s (t) = V cos( Mrad/s t) V cos(0 Mrad/s t). Using simple Bode Plots, determine the smallest N required to reduce the higher frequency signal by 80 db while leaving the lower frequency signal unchanged. What is the value of the pole of each section? Now, using the transfer function of the filter so obtained, find the actual attenuation of the two signals. ecompute N and the pole of the filter if the lower frequency should be attenuated by 3 db and the higher frequency by 80 db. 3. (3 pts.) Design an ac coupling stage between the

9 2 V dc bias=v stage ac coupling stage 2 i = pf Figure 3: two stages shown in Fig. 3. The second stage has an input capacitance i = pf. a) The attenuation for very high frequencies (ω ) should be less than db, b) The attenuation for 0 Mrad/s should be less than 4 db, c) The capacitor used in the circuit should be minimized. d) The dc bias provided to the 2nd stage should be V (A V dc source is available to you.). 4. ( pt.) Design a filter with the transfer function k/( s/p ), with k = 0, p = 0 Mrad/s. Draw the schematic with ideal opamps use = pf. (2 pts.) Determine the dc gain A o and the unity gain frequency ω u of the opamp such that each of these nonidealities (acting by itself) changes the pole of the filter by less than 2.5%. (2 pts.) Draw the Bode plot of the loop gain for the filter you designed. Use an integrator model for the opamp with ω u determined previously. (2 pts.) edesign the filter (use ideal opamps) assuming that the largest resistor allowed is 0 kω.

10 E425: Analog Filter Synthesis and Design: HW5 due on 25 Feb V s s L L two circuits. s =pf L Figure : V s. (2 pts.) Determine (s)/ (s) for the filter in Fig.. For a given s, determine L such that Q is maximum. What is the maximum Q? What is ω p under this condition? V s s L =pf L Figure 2: 2. (2 pts.) What is the bandwidth of the circuit in Fig. 2? If you were allowed to place a series inductor L as in Fig. 2, what value would you choose for it to maximize the bandwidth without introducing peaking in the magnitude response? What is the resulting bandwidth? Sketch the frequency responses of the Figure 3: 3. (4 pts.) For each of Fig. 3 and Fig. 3, Assuming s = 0 determine L and so that a bandpass filter with ω p /2π = 5 GHz and a 3dB bandwidth of GHz is realized. If v s (t) is a V sinusoid at 5 GHz, what is the current flowing through the input source? (c) What is the value of s, the source resistance, that results in a 0% deviation in Q? 4. (5 pts.) In Fig. 4 consider two cases = 2 = and = 2, 2 = /2. For each of these, Find V (s)/ (s) Is there a difference? Evaluate V k (s)/ (s), k = {2, 3} Is there a difference? What is the maximum of V k (jω)/ (jω)? (c) The input is a sinusoid v i (t) = p cos(ωt) where ω can be This means that ω p = 2π 5 Grad/s

11 2 V 3 5 OPA3 2 OPA V OPA2 V2 Figure 4: anything. If the opamps have a swing limit of V, what is the largest p that can be applied while maintaining all the opamps in the linear region? 5. (3 pts.) Design a second order g m Butterworth filter with dc gain= and 3dB bandwidth= MHz. Assume that the smallest g m is 0 µs. Give the transfer function and all the component values in the g m filter schematic. (4 pts.) Using the above filter as the basis, design a lowpass notch filter with dc gain=0 and a notch at 0 MHz. Use the voltage summing technique. Give the transfer function and all the component values in the g m filter schematic. What is the high frequency gain of this filter? What is the attenuation of the filter at MHz w.r.t. dc? Has the 3dB bandwidth increased or decreased compared to the filter in?

12 E425: Analog Filter Synthesis and Design: HW6 due on 4 Mar In addition to the problems here, problem #5 from HW5 is also due on 4 Mar (33 pts.)epeat the design in problem #5 of HW5 using opamps and feedforward technique. Use 0 pf capacitors. Design the Butterworth lowpass filter. g m Figure 2: L=H 2 Obtain the lowpass notch transfer function at the output V. (c) Obtain the lowpass notch transfer function at the output V 2. g mi g m2i V g m /Q Figure : g m g m 2. (2 pts.) In Fig., Determine the transfer functions from and 2 to voltages V and V 2. output of OPA; in the handout Transfer functions realizable in a biquad. V 2 3. (2223 pts.) Design a H inductor using transconductors and a 00 pf capacitor. Derive the (passive) equivalent circuit of the previously designed inductor if the capacitor had a MΩ resistor across it. (c) Design an L bandpass filter with ω p = 00 krad/s and Q = 0 using a H inductor. The gain at the resonant frequency should be 0. Use the topology in Fig. 2. (d) eplace the inductor with the equivalent circuit obtained in and reevaluate the transfer function (s)/ (s) What, if any, is the deviation from the intended design in (c). (e) How would you change the design to restore the Q to 0? You cannot remove the MΩ resistor which is across the capacitor. (f) Simulate (i) the circuit in Fig. 2, (ii) the circuit with the inductor replaced by the active inductor 2, and (iii) the repaired circuit from (e). 2 use the circuit with transconductors and capacitors, not the equivalent obtained in ; Include the MΩ resistor across the

13 2 Submit the magnitude and the phase responses; overlay the responses of the three circuits. 00 pf capacitor.

14 E425: Analog Filter Synthesis and Design: HW7 due on 25 Mar For 5, give the schematic of the passive filter with all the element values. For 3, give the the transfer function in the normalized form which is b 0 b (s/q/ω n ) b 2 (s/ω n ) 2 s/q/ω n (s/ω n ) 2 where ω n is a convenient normalizing frequency. For 35, give the expression for the frequency transformation along with the numerical values for the parameters in the transformation. For 6, give the final schematic and explain very briefly the purpose of each feedforward component.. ( pt.) Design a second order passive low L Figure : 2 pass L notch filter with Q = / 2, ω p = Mrad/s and a transmission zero at ω z = 0 Mrad/s. Use the topology in Fig. with 2 = 0 nf. What is the attenuation in db at Mrad/s? all this A p. 2. (2 pts.) Scale the filter in () so that it uses = Ω and has a notch at 0 rad/s. Elements from the input to various opamps. What is the frequency Ω p at which the attenuation is A p? What is the smallest frequency 2 at which the attenuation is A s = 20 db? all this Ω s. 3. (3 pts.) Transform the prototype in (2) to a passive L highpass filter with an attenuation A p (determined in ()) at 0 Mrad/s and a termination impedance 0 kω. What is the frequency of the notch in this filter? Draw the schematic replacing the inductors with capacitively terminated gyrators whose gyration resistance is 0 kω. 4. (4 pts.) Transform the prototype in (2) to a passive L bandpass filter whose attenuation is A p at ω p = 0 Mrad/s and ω p2 = 2. Mrad/s. The termination impedance should be 0 kω. What are the stopband edges ω s and ω s2 where the attenuation is A s? What is the gain of the filter at Mrad/s? If one of the notches of the filter is at 4.7 Mrad/s, where is the other notch? 5. (4 pts.) Transform the prototype in (2) to a passive L bandstop filter whose attenuation is at least A s in the range 8 Mrad/s ω 00 Mrad/s. Use a termination impedance of kω. What are the passband edges ω p and 2 You can calculate this analyticallyyou ll get a 2 nd order equation in Ω 2 ; or determine it using simulationbe sure to use a sufficiently small frequency step.

15 2 ω p2 where the attenuation is A p? What is the filter s attenuation at 90 Mrad/s? 6. (2 pts.) ealize an an opamp version of the highpass filter in (3). Use the TowThomas biquad with feedforward technique to realize the zeros at the output of the first opamp. Use = 0 kω in the resonator core. 7. ( pt.) ealize a bandpass filter whose attenuation is A p at f p = 0 MHz and f p2 = 2. MHz. (Hint: You don t have to go through the whole synthesis again. Use the result from (4)). 8. (2 pt.) Simulate the magnitude response of the passive circuits in, 3 (not the part with the gyrator), 4, 5. (Plot all 4 magnitude responses in 4 subwindows of the same plot for submission. Use appropriate ranges for x and y axes to show all points of interest). In each, mark the frequency of the notch(es). 9. ( pt.) Simulate the magnitude response of the opamp filter in 6. For the opamps use ideal voltage controlled voltage sources with gain=0 6.

16 E425: Analog Filter Synthesis and Design: HW8 due on 8 Apr transconductance=s =/ω p = b I b 0 I transconductance=s =/ω p =Q L=/ω p b 2 I b I b 0 I L I I I I I L "bilinear" "biquad" Figure :. (5 pts.) ompute the transfer functions / in terms of the parameters (Q, ω p, b 0, b, b 2 ) for the circuits in Fig. (a, b). Turn these circuits into parameterized subcircuits bilinear and biquad in cadence with the required parameters. You can then use these subcircuits to realize ideal cascade realizations of any transfer function. 0dB db 40dB 0dB db 40dB 2MHz 4MHz rad/s 2 rad/s Figure 2: 2. You are required to realize a filter that meets the specifications shown in Fig. 2. You are given (Table ) In cadence, to realize a current controlled voltage source, you also need to have a 0 V voltage source through which the desired current is flowing. See the example subcircuit lpf in the library E425 examples.

17 2 the poles and zeros of 4 types (Excluding Bessel) of filters which satisfy the prototype specifications in Fig. 2. (4 pts.) Tabulate the order, the resonant frequencies, the quality factors of the poles, and the location of transmission zeros (if present) of the different types of filters that satisfy the specs. in Fig. 2. (7 pts.) Using the parameterized subcircuits for the bilinear and the biquadratic filters, simulate the four filters (using the cascade structure) in cadence. Use the rules of cascading discussed in the class. You do not have to submit the schematics. learly state the order of cascade and the pole zero pairing. Plot their magnitude and phase responses 2, and the group delay (for this, you can use the function groupdelay in the calculator in cadence). (c) (4 pts.) For each filter, determine the maximum transfer function magnitude from the input to each of the stage (first or second order) outputs. If each output were limited to V, what is the maximum input voltage that could be applied to each without having distortion? (d) (4 pts.) Simulate the transfer function of the Bessel filter prototype (last column of Table ) using the same technique as above. If this filter were scaled such that it had an attenuation A s = 40 db at 4 MHz (the stopband edge), what would be its attenuation at the passband edge (2 MHz)? 3 Does it meet the specs in Fig. 2? (e) (4 pts.) For each of the 4 filters that satisfies the specs in Fig. 2, list the maximum quality factor of the biquad stages used, the maximum resonant frequency, and the maximum group delay variation in the passband (< 2 MHz). (2 pts.) epeat 3 for the Bessel filter. To find its maximum resonant frequency, calculate the maximum resonant frequency in the prototype and multiply it by the scaling factor determined above. Table : Prototype zeros and poles Butterworth hebyshev Inverse hebyshev Elliptic Bessel poles poles zeros poles zeros poles poles.03 ± j ± j0.990 ±j ± j.03 ±j ± j ± j ± j ± j0.69 ±j ± j0.875 ±j ± j ± j ± j ± j ± j ± j ± j Plot the magnitude responses of the 4 filters in the same plot; same for the phase response and the group delay. Plot the magnitude response (in db) twice once showing the whole picture and once zoomed in on the passband. Use sensible scales so that the details of the response can be seen. e.g. with notches, the response goes down to db and the default scale may be totally unsuitable. 3 You don t need to rescale the filter and simulate. You should be able to answer this by looking at the prototype response.

18 E425: Analog Filter Synthesis and Design: HW9 due on 5 Apr Design and simulate the following active versions of the Inverse hebyshev filter (scaled to a 2 MHz passband) given in HW8. Start with all resistors of 0 kω or all g m of 00 µs. Scale the circuit to have equal maxima in the ac response of all opamp/g m outputs. Submit the schematic with all the component values and the magnitude response plots before and after scaling. Plot the output magnitudes of all the outputs in a given filter on the same plot.. (0 pts.) ascade of opamp biquad stages zeros using feedforward. 2. (0 pts.) g m ladder filter. Table : Inverse chebyshev prototype zeros and poles: passband corner = rad/s Inverse hebyshev zeros poles pole resonant frequency pole quality factor ±j ± j ±j ± j n/a n/a Ω.2496H.0290H Ω Vi F F Vo F.5592F 0.284F Figure : Inverse chebyshev doubly terminated ladder prototype with poles and zeros shown in Table

19 E425: Analog Filter Synthesis and Design: HW0 due on 29 Apr v n =V p cos(ωt) v i α 3 v i 3 Σ v n =V p cos(ωt) k v i α 3 v i 3 Σ /k Figure :. (423 pts.) Fig. shows a block that has third order distortion and an output noise v n (rms volts). It could represent a filter or any other circuit that has distortion and noise. The input is a sinusoid with a peak V p. In Fig. (a, b) calculate the following quantities at the output: Peak value of the fundamental sinusoid, amplitude of the third harmonic, rms output noise, ratio of the third harmonic peak to the fundamental peak, ratio of rms noise to rms fundamental. Neglect the contribution from the v 3 i term while calculating the output fundamental amplitude. How does k affect the noise/signal and distortion/signal ratios? What would you do with k to minimize noise/signal, distortion/signal? Give a very brief intuitive explanation. ompute k such that noise/signal and distortion/signal ratios are equal. (c) If α 3 = V 2, v n = 2mV, rms, V p = V, calculate k for equal noise/signal and distortion/signal ratios. With these numerical values, calculate the noise/signal and distortion/signal ratios in Fig. (a, b). How do the two circuits compare? 2. (2322 pts.) = /2πnF, = kω, L = 0/2π µh. alculate the output noise voltage of the circuit in Fig. 2. Simulate the noise in Fig. 2. To compute the mean squared noise, integrate the spectral density from i) /0 the 3 db bandwidth to 0 times the 3 db bandwidth, and ii) /00 the 3 db bandwidth to 00 times the 3 db bandwidth. How different are the two values? signal implicitly means desired signal, in this case the fundamental.

20 2 L V o Figure 2: (c) Simulate the noise in Fig. 2. To compute the mean squared noise, integrate the spectral density in the range f 0 ± 0f B where f 0 is the center frequency and f B is the 3 db bandwidth of the bandpass filter. (d) Set L = 0./2π µh and repeat the previous simulation. (e) ompare the noise in the three cases above. What is the bandwidth of the circuit in the three cases? Does the value of the mean squared noise make sense, considering that it is the spectral density integrated over a certain bandwidth? 3. (442 pts.) The input referred noise voltage of a transconductor g m is γ4kt/g m. i n, i n, g m,opa v n,gm g m i n,gm g m i n,gm Figure 3: alculate g m,op A in Fig. 3 if the loop gain has to be 00 (HW2 had problems related to the use of a transconductor as an opamp). alculate 2 the noise spectral density at the output in Fig. 3(a, b) in terms of kt, g m, g m,op A,, γ. (c) In the expression for Fig. 3 substitue the value of g m,op A calculated in (i). In the expression for Fig. 3 substitute g m = /. What can you say about the relative values of noise in Fig. 3 and Fig. 3 assuming e.g. γ = 5. The comparison is typically true for opamp and g m filters. (d) If = V p cos(ωt) what is the peak current driven by each active component in Fig. 3? 2 It is easiest if you represent the noise of different components as shown. While analyzing Fig. 3, you can assume an opamp with infinite gain.

21 E425: Analog Filter Synthesis and Design: Project Equalizer for Gb/s data due on 6 May 2003 Description 2.5V V V B channel transmitter (lowpass) A Σ input Equalizing filter output clk( GHz) 00mV clock feedthrough Figure : Transmitter, channel, and the equalizer Digital data at f s = Gb/s from a transmitter (Fig. ) passes through a lowpass channel which attenuates some of the high frequencies of the signal. Additionally, some of the clock at f s = GHz leaks to the data output. Your job is to design an equalizing filter to boost the high frequencies of the signal around f s /2 = 500 MHz and filter the clock feedthrough at f s = GHz. The filter is required to have a linear phase. For linear phase, start with a seventh order Bessel filter with a 3 db bandwidth of f s /2 = 500 MHz. Add a pair of complex conjugate zeros and a pair of equal and opposite real zeros to obtain a 3 db boost at f s /2 = 500 MHz and 0 db attenuation at f s = GHz. You can use any topology that strikes your fancy: opamp or g m ; ladder or cascade; single ended or differential. The total capacitance used in your filter must be 2.xx pf where xx are the last 2 digits of your social security number. The dc gain of the filter must be 0 db.

22 2 2 Project submission. Give a clear description of the following in your report. Prototype lowpass filter design; computation of zeros to get the boost at f s /2 and attenuation at f s. Detailed design of the filter at the desired frequency with all the resistor/g m and capacitor values. Scaling the filter to have equal maxima in the ac response at all opamp/g m outputs. Scaling the filter to use a total capacitance of 2.xx pf. A complete schematic with all the component values. Use a sensible hierarchy so that the design is understandable. 2. Before the due date (6 May 2003, 5pm) me your cadence library path that contains the project, and the name of the topmost cell in your hierarchy. 3. Submit the following simulation results. Frequency response: magnitude response at the filter s output showing the gain boost at f s /2 and the attenuation at f s ; group delay response; plot with overlaid magnitude response at all the opamp/g m outputs. Transient: Show the response of the filter for a single V pulse whose duration is /f s = ns. You will be given the waveforms of the bit streams at A and B. Simulate the filter with its input being the sum of the channel output and the clock feedthrough (00 mv sinusoid at GHz). Show the outputs of the transmitter and the channel (waveforms will be given to you) and the output of the filter. Briefly describe what your filter has done to the signal. Noise: Show the noise spectral density at the output. ompute the integrated noise upto f s = GHz. alculate the output signal to noise ratio, assuming that a V sinusoid at low frequencies is applied to the filter. Power dissipation: Plot the frequency response magnitude (with an input magnitude of V) of the output currents of the each of the opamp/g m. Tabulate the maximum of each of the current magnitudes over frequency. These will be the largest currents drawn from each opamp/g m. If you are using opamps, take the largest of these and multiply by 8. This will be the current drawn per opamp. Multiply by the number of opamps to arrive at the total current dissipation. This means that you are using identical opamps which are capable of driving the largest current demanded in this circuit. This is a common situation in filter design. If you are using g m s, multiply the largest current drawn from each g m, by 8 and sum the result to obtain the total current dissipation. Note that you cannot in general use identical g m s as the transfer function depends on the value of the g m s. ompute the power dissipation assuming that the supply voltage is 2.5 V.

23 3 3 Simulation/modeling You can generate a voltage source with an arbitrary waveform using the voltage source vpwlf in the library analoglib. You need to specify a file that has the voltage values at certain time points. /u2/nagi/courses/e425/project/tx output.dat and /u2/nagi/courses/e425/project/channel output.dat have the transmitter and the channel outputs respectively. Model the clock feedthrough using a 00 mv sinusoid at f s = GHz in series with the input voltage source. Use the subcircuits in Fig. 2 to model g m s and opamps. You can make these into subcircuits (parameterized if necessary) and use them. The GΩ resistors are there to provide dc paths to ground and suppress warnings from the simulator about floating nodes. They will not affect the operation of the circuit if you have calculated the component values in your circuit correctly). The resistor in series with the negative input of the cells is for modeling the noise of the opamps/g m s. They too will not affect the operation of your circuit as the current flowing through them is negligible. GΩ in v 4/g m (noise) g m v GΩ out in GΩ v 4/g m (noise) 0.5GΩ g m v g m v 0.5GΩ out in GΩ v 25Ω (noise) 000v out in GΩ v 25Ω (noise) 500v 500v out (c) (d) Figure 2: Single ended g m, Differential g m, (c) Single ended opamp, (d) Differential opamp. 4 Timeline There are 4.5 weeks to the project deadline. Budget 2 weeks for design and 2 weeks for simulation and writing the report. The design can be started with what you have learned in the class so far. For the prototype filter you can consult A. I. Zverev, Handbook of Filter Synthesis, Wiley, New York, 967, which is a non circulating reference in the Engineering library.