EECS140 Fall 2009 2008 HW2 Due 8 10 09 8am in the box on the 2nd floor 1 The Microlab on the 4th floor of Cory Hall is arguably the world s greatest research clean room While we sometimes hold the record for the smallest or the fastest transistors in the world there is also a regular standard CMOS run for characterization purposes The report from a recent run is available online at http www eecs berkeley edu Pubs TechRpts 2008 EECS 2008 168 pdf Looking at section 4 2 you can see some of the measured results from this run As you make the estimates below spend some time thinking about the best method to make the estimate but don t worry too much about accuracy a From Figure 5 estimate k for the NMOS and PMOS devices b From Figure 5 estimate the threshold voltage of the NMOS and PMOS devices as a function of the source to bulk voltage What is Vt0 and what s a rough estimate for gamma for these devices c From Figure 6 what s a rough estimate of the transconductance per amp gm Id of the NMOS devices in the weak inversion sub threshold region Roughly what is the range of currents for which the NMOS device is in weak inversion What does that mean about the range of transconductance d From Figure 7 plot the saturation drain current vs the gate voltage Does this look like a quadratic device e From Figure 7 estimate the output resistance in saturation when Vg is two or three volts Estimate lambda f From Figure 8 what s a rough estimate of the percentage variation in Vt from die to die It s common for device parameters like Vt to vary linearly with position across a wafer Do you see that in Appendix C 2 Intel s latest 32nm technology was presented at the IEDM conference recently http www intel com technology architecture silicon 32nm 32nm htm Using Figure 5 in this paper a estimate gm and ro for the NMOS and PMOS devices when Vgs is 0 7V b What would the gain be if I made an NMOS common source amplifier out of this device using a perfect current source load c What would the gain be for an NMOS common source amplifier with a PMOS load using these devices Assume a 1V supply and a PMOS bias voltage of 0 4V 3 Using the standard ee140 0 5um CMOS process models assume that you want to design a transistor to have a transconductance gm 1mS You may also ignore the effect of lambda assume it s zero for this problem only a If you pick the current through the transistor to be 1mA what will the overdrive voltage and the W L ratio be if the device is NMOS PMOS b If you pick the overdrive voltage Vov 200mV what will the current and W L ratio be if the device is NMOS PMOS c If you fix the geometry to be 50u 0 5u what will the current and overdrive voltage be if the device is NMOS PMOS d What is the minimum current that will give me this transconductance in any device in this process What device type N or P overdrive voltage and size will that correspond to e What is the smallest device that can have this transconductance 4 Draw an RC low pass filter with a 10k resistor and a 100fF capacitor a What is the time constant of this filter What is the angular frequency c radians second at which the capacitor has the same magnitude of impedance as the resistor What is the pole frequency fc Hz How are these terms related b Draw by hand a cycle or two of the input and output voltages of this filter when driven by a 1V amplitude sine wave with 3 different frequencies 0 1 1 10 fc Concentrate on getting the phase and amplitude correct c Draw by hand a cycle or two of the input and output voltages of this filter when driven by a 1V amplitude square wave with the same frequencies Concentrate on getting the slope correct at the rising and falling edges of the input 5 For the common source NMOS amplifier with a PMOS load shown below a Calculate the current flowing in the PMOS device when the output is at mid rail 1 5V You must take channel length modulation into account b Calculate the gate bias needed on the NMOS device to keep the output at mid rail c Calculate gm ro Cgs Cgd Cdb for each transistor at this bias point Are both devices in saturation d Use the op command to get SPICE to calculate the same parameters and compare your answers with what SPICE calculates showing percent error 3V 2V 50u 1u Vout Vi 50u 1u
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