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© Digital Integrated Circuits 2nd Inverter EE4271 VLSI Design The Inverter Dr. Shiyan Hu Office: EERC 518 shiyan@mtu.edu Adapted and modified from Digital Integrated Circuits: A Design Perspective by Jan M. Rabaey, Anantha Chandrakasan, and Borivoje Nikolic.

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© Digital Integrated Circuits 2nd Inverter Pass-Transistors Need a circuit element which acts as a switch When the control signal CLK is high, Vout=Vin When the control signal CLK is low, Vout is open circuited We can use NMOS or PMOS to implement it. For PMOS device, the polarity of CLK is reversed. NMOS based PMOS based

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© Digital Integrated Circuits 2nd Inverter NMOS Pass Transistors Initially Vout=0. input=drain, output=source When CLK=0, then Vgs=0. NMOS cut-off When CLK=Vdd, If Vin=Vdd (Vout=0 initially), Vgs>Vt, Vgs-Vt=Vdd-Vt<=Vds=Vdd, NMOS is in saturation region as a transient response and C L is charged. When Vout reaches Vdd-Vt, Vgs=Vdd-(Vdd-Vt)=Vt. NMOS cut-off. However, if Vout drops below Vdd-Vt, NMOS will be turned on again since Vgs>Vt. Thus, NMOS transmits Vdd value but drops it by Vt.

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© Digital Integrated Circuits 2nd Inverter NMOS Pass Transistors - II If Vin=0 (and CLK=Vdd), source=input, drain=output If Vout=Vdd-Vt (note that it is the maximum value for Vout for the transistor to be on), Vgs=Vdd>Vt, Vds=Vdd- Vt=Vgs-Vt The NMOS is on the boundary of linear region and saturation region C L is discharged As Vout approaches 0, the NMOS is linear region. Thus, Vout is completely discharged. When Vout=0, Vds=0 and Ids=0, thus, the discharge is done. NMOS pass transistor transmits a 0 voltage without any degradation

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© Digital Integrated Circuits 2nd Inverter PMOS Pass Transistors Similar to NMOS pass transistor Assume that initially Vout=0 When CLK=Vdd, PMOS cut-off When CLK=0, If Vin=Vdd, PMOS transmits a Vdd value without degradation If Vin=0, PMOS transmits a 0 value with degradation, Vout=|Vt|

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© Digital Integrated Circuits 2nd Inverter Transmission Gate An NMOS transmits a 0 value without degradation while transmits a Vdd value with degradation A PMOS transmits a Vdd value without degradation while transmits a 0 value with degradation Use both in parallel, then can transmit both 0 and Vdd well. CLK=0, both transistors cut-off CLK=Vdd, both transistors are on. When Vin=Vdd, NMOS cut-off when Vout=Vdd-Vtn, but PMOS will drag Vout to Vdd. When Vin=0, PMOS cut-off when Vout=|Vtp|, but NMOS will drag Vout to 0.

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© Digital Integrated Circuits 2nd Inverter Propagation Delay

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© Digital Integrated Circuits 2nd Inverter Rising delay and Falling delay Rising delay tr=time for the signal to change from 10% to 90% of Vdd Falling delay tf=time for the signal to change from 90% to 10% of Vdd Delay=time from input signal transition (50% Vdd) to output signal transition (50% Vdd).

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© Digital Integrated Circuits 2nd Inverter Delay

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© Digital Integrated Circuits 2nd Inverter Inverter falling-time

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© Digital Integrated Circuits 2nd Inverter NMOS falling time For NMOS 1.Vin=0, Vgsn=0

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© Digital Integrated Circuits 2nd Inverter NMOS falling time When Vin=Vdd, instantaneously, Vgsn=Vdd tf=tf1+tf2 tf1: time for the voltage on C L to switch from 0.9Vdd to Vgsn- Vtn=Vdd-Vtn tf2: time for the voltage on C L to switch from Vdd-Vtn to 0.1Vdd tf1 tf2

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© Digital Integrated Circuits 2nd Inverter NMOS falling time For tf1: Integrate Vout from 0.9Vdd to Vdd-Vt For tf2, we have Vgsn=Vdd Vdsn=Vout

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© Digital Integrated Circuits 2nd Inverter NMOS falling time tf=tf1+tf2 Assume Vt=0.2Vdd

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© Digital Integrated Circuits 2nd Inverter Rising time Assume |Vtp|=0.2Vdd

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© Digital Integrated Circuits 2nd Inverter Falling and Rising time Assume Vtn=-Vtp, then we can show that Thus, for equal rising and falling time, set That is, Wp=2Wn since up=un/2

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© Digital Integrated Circuits 2nd Inverter Power Dissipation

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© Digital Integrated Circuits 2nd Inverter Where Does Power Go in CMOS?

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© Digital Integrated Circuits 2nd Inverter Dynamic Power Dissipation Power = C L * V dd 2 * f Need to reduce C L, V dd, andf to reduce power. VinVout C L Vdd Not a function of transistor sizes

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© Digital Integrated Circuits 2nd Inverter Dynamic Power Dynamic power is due to charging/discharging load capacitor C L In charging, C L is loaded with a charge C L Vdd which requires the energy of QVdd= C L Vdd 2, and all the energy will be dissipated when discharging is done. Total power = C L Vdd 2 If this is performed with frequency f, clearly, total power = C L Vdd 2 f

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© Digital Integrated Circuits 2nd Inverter Dynamic Power- II If the waveform is not periodic, denote by P the probability of switching for the signal The dynamic power is the most important power source It is quadratically dependant on Vdd It is proportional to the number of switching. We can slow down the clock not on the timing critical path to save power. It is not dependent of the transistor itself but the load of the transistor.

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© Digital Integrated Circuits 2nd Inverter Short Circuit Currents Happens when both transistors are on. If every switching is instantaneous, then no short circuits. Longer delay -> larger short circuit power

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© Digital Integrated Circuits 2nd Inverter Short-Circuit Currents

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© Digital Integrated Circuits 2nd Inverter Leakage Sub-threshold current one of most compelling issues in low-energy circuit design.

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© Digital Integrated Circuits 2nd Inverter Subthreshold Leakage Component

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© Digital Integrated Circuits 2nd Inverter Principles for Power Reduction Prime choice: Reduce voltage Recent years have seen an acceleration in supply voltage reduction Design at very low voltages still open question (0.5V) Reduce switching activity Reduce physical capacitance

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© Digital Integrated Circuits 2nd Inverter Impact of Technology Scaling

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© Digital Integrated Circuits 2nd Inverter Goals of Technology Scaling Make things cheaper: Want to sell more functions (transistors) per chip for the same money Build same products cheaper, sell the same part for less money Price of a transistor has to be reduced But also want to be faster, smaller, lower power

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© Digital Integrated Circuits 2nd Inverter Scaling Goals of scaling the dimensions by 30%: Reduce gate delay by 30% Double transistor density Die size used to increase by 14% per generation Technology generation spans 2-3 years

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© Digital Integrated Circuits 2nd Inverter Technology Scaling Devices scale to smaller dimensions with advancing technology. A scaling factor S describes the ratio of dimension between the old technology and the new technology. In practice, S=1.2-1.5.

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© Digital Integrated Circuits 2nd Inverter Technology Scaling - II In practice, it is not feasible to scale voltage since different ICs in the system may have different Vdd. This may require extremely complex additional circuits. We can only allow very few different levels of Vdd. In technology scaling, we often have fixed voltage scaling model. W,L,tox scales down by 1/S Vdd, Vt unchanged Area scales down by 1/S 2 Cox scales up by S due to tox Gate capacitance = CoxWL scales down by 1/S scales up by S Linear and saturation region current scales up by S Current density scales up by S 3 P=Vdd*I, power density scales up by S 3 Power consumption is a major design issue

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© Digital Integrated Circuits 2nd Inverter Summary Inverter Five regions Transmission gate Inverter delay Power Dynamic Leakage Short-circuit Technology scaling

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