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

Pass-Transistors NMOS based PMOS based 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

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 CL 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.

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 CL 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

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|

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.

Propagation Delay

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).

Delay

Inverter falling-time

NMOS falling time S D V C in out L DD For NMOS Vin=0, Vgsn=0<Vt, Vdsn=Vout=Vdd, NMOS is in cut-off region, X1 Vin=Vdd, instantaneously, Vgsn=Vdd>Vt,Vdsn=Vout=Vdd, Vgsn-Vtn=Vdd-Vtn<Vdd, NMOS is in saturation region, X2 The operating point follows the arrow to the origin. So Vout=0 at X3. V in out C L DD S D

NMOS falling time tf1 tf2 When Vin=Vdd, instantaneously, Vgsn=Vdd tf=tf1+tf2 tf1: time for the voltage on CL to switch from 0.9Vdd to Vgsn-Vtn=Vdd-Vtn tf2: time for the voltage on CL to switch from Vdd-Vtn to 0.1Vdd tf1 tf2

NMOS falling time Vgsn=Vdd Vdsn=Vout For tf1: Integrate Vout from 0.9Vdd to Vdd-Vt For tf2, we have

NMOS falling time tf=tf1+tf2 Assume Vt=0.2Vdd

Rising time Assume |Vtp|=0.2Vdd

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

Power Dissipation

Where Does Power Go in CMOS?

Dynamic Power Dissipation Vin Vout C L Vdd Power = C * V 2 * f L dd Not a function of transistor sizes Need to reduce C , V , and f to reduce power. L dd

Dynamic Power Dynamic power is due to charging/discharging load capacitor CL In charging, CL is loaded with a charge CL Vdd which requires the energy of QVdd= CL Vdd2, and all the energy will be dissipated when discharging is done. Total power = CL Vdd2 If this is performed with frequency f, clearly, total power = CL Vdd2 f

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.

Short Circuit Currents Happens when both transistors are on. If every switching is instantaneous, then no short circuits. Longer delay -> larger short circuit power

Short-Circuit Currents

Leakage Sub-threshold current is one of most compelling issues in low-energy circuit design.

Subthreshold Leakage Component

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

Impact of Technology Scaling

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

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

EE141 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. 30

Technology Scaling - II EE141 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/S2 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 S3 P=Vdd*I, power density scales up by S3 Power consumption is a major design issue 31

Summary Inverter Transmission gate Inverter delay Power EE141 Summary Inverter Five regions Transmission gate Inverter delay Power Dynamic Leakage Short-circuit Technology scaling 32