CIRCUIT DESIGNER’S NOTEBOOKCapacitors in Bypass Applications

Figure 1: Bypass Capacitor Configuration

Capacitors used in bypass applications areimplemented as shunt elements and serve to carryRF energy from a specific point in the circuit toground. Proper selection of a bypass capacitor willprovide a very low impedance path to ground. Intheory the ideal impedance is zero ohms; howevera real capacitor will exhibit some impedance dueto its reactance and inherent parasitic elements.Satisfying capacit ive bypass applicationrequirements entails careful analysis of variousfrequency dependent capacitor parameters such asseries resonant frequency (FSR), equivalent seriesresistance (ESR), and the magnitude of theimpedance. The ESR and impedance shouldalways be evaluated at the operating frequency.

Figure 1 is a block diagram illustrating a capacitorbypass application. Capacitor C0 in this figure isrepresented with its equivalent series resistancedenoted as RS, equivalent series inductance (ESL)denoted as LS and parasitic parallel capacitance CP,associated with the parallel resonant frequency (FPR).

Terminology:Equivalent Series Resistance (ESR): Is the summationof all losses resulting from the dielectric (RSD) andmetal elements (RSM) of a capacitor (RSD + RSM ) andis typically expressed as milli-ohms. RSD is thedielectric loss tangent and is dependent upon specificcharacteristics of the dielectric formulation andprocessing. Metal losses are dependent on resistivecharacteristics of the electrode and terminationmaterials, as well as the losses of the electrodes dueto skin effect. ESR is a key parameter to considerwhen utilizing capacitors in RF bypass applications.

Quality factor (Q): A capacitor’s Q is numericallyequal to the ratio of its net reactance (XC - XL) to itsequivalent series resistance (ESR) or Q = |XC - XL| /ESR. From this expression it can be seen that thecapacitor’s Q varies inversely to its ESR anddirectly with its net reactance.

Series Resonant Frequency (FSR): A resonance thatoccurs at FSR =1/2� . At this frequency thecapacitor’s net reactance is zero and theimpedance is equal to the ESR. The capacitor willprovide its lowest impedance path required foroptimal bypassing at this frequency.

Parallel Resonant Frequency (FPR): A resonanceoccurring at approximately twice the FSR for aparallel plate capacitor. In contrast to FSR theimpedance of a capacitor at its FPR can beprecipitously high. This is readily observed byassessing the magnitude of the insertion loss at FPR.

Impedance: (Z ) The magnitude of a capacitor’simpedance is equal to . Asseen by this relationship a capacitor’s impedance issignificantly influenced by its net reactance (XL-XC).

Figure 2: Impedance vs. Frequency forATC100A101 (100pF)

It is important to evaluate the magnitude of theimpedance throughout the desired frequencyrange. A properly selected bypass capacitor willexhibit suitably low impedance over this range. Asseen in Figure 2 the net impedance below FSR iscapacitive and is dominated by 1/�C, yielding ahyperbolic curve for frequencies less than FSR.Conversely, the net impedance above FSR isinductive and is dominated by �L yielding a linearline segment for frequencies greater than FSR.

Application ExampleBypassing is a critical design matter that requirescareful consideration. Figure 3 shows a 1.9 GHzcellular FET amplifier with emphasis on the drainbias network.

Figure 3: Bypass Capacitors in a 1.9GHz FETBroadband Bias Network

The circuit elements depicted in this figure willserve to suppress RF energy from getting onto theVDD supply line while providing high impedance atthe drain in order to maintain optimum in-band RFgain. It also functions to keep noise generated bythe power supply from appearing on the drain ofthe FET. High-speed switching environmentscreated by switch mode power supplies (SMPS) willgenerate noise on VDD supply lines. Instantaneouscurrent generated by fast rising and falling switchpulse edges can easily cause the VDD supply line toring. The resultant noise can include frequencies ofup to several hundred megahertz. RF noisegenerated by SMPS switching is continuous andwill generally occur up to frequencies equal to0.35 / PE, where PE = pulse rise or fall time (sec).

For example a switched pulse with a rise and fallt ime of 1.5 ns will yield spurious spectralcomponents up to 233 MHz.

Drain Bias Network:As illustrated in figure 3, the FET’s drain bias networkconsists of series inductive elements having animpedance of �L and shunt capacitive elements withan impedance of 1/�C. Proper selection of bypasscapacitors in the bias network is essential as they willserve to de-couple RF energy from the VDD supply lineto ground over a wide range of frequencies.

Since capacitors exhibit a small parasit icinductance there is an associated series (self )resonant frequency where FSR = 1/2� . AtFSR the magnitude of the inductive and capacitivereactances are equal and hence the net impedance

is equal to a small ESRvalue. Accordingly the designer will ideally selecta capacitor that has an FSR at or close to thedesired “bypass frequency”. This preference isbased on establishing a low impedance path withminimal or zero net reactance thereby making itideal for bypassing applications.

FPR usually occurs at more than twice FSR for mostmulti-layer ceramic capacitors. At the capacitor’sFPR, the impedance is likely to be high andinductive (R+j �L) and may not provide anadequate RF path to ground. To alleviate this,several capacitors are selected such that their self-resonant frequencies are staggered in order tocover a wide range of frequencies with reasonablylow loss. The number of required capacitiveelements depends on the loss and impedancecharacteristics of each element over the intendedfrequency band segments.

The inductors are in series with the drain and arenot directly connected to reference RF ground.Accordingly they rely on bypass capacitors, C1through C4 to achieve a low impedance path toground. The combination of L1 and C1 will greatlysuppress the in-band 1.9 GHz carrier frequencyenergy from appearing on the VDD supply line.Inductor L1 will act as a block at this frequencywhile capacitor C1 will serve to further suppress in-band RF energy by bypassing it to ground. L2 C2,C3 and C4 will suppress RF energy at frequenciesbelow the 1.9 GHz carrier frequency where thegain of the amplifier may be much higher. C1’scapacitance value is selected such that its FSR isclose to the amplifiers operating frequency. SinceC1 is a shunt element, and the impedance is low atits FSR, the RF energy at the operating frequencywill be bypassed to ground. Capacitor elements C2,C3 and C4 are staggered in value and selected sothat the impedance of each will be low atsuccessive frequency segments in order to offercontinuous bypassing of frequencies below theamplifier’s operating band.

Richard FioreDirector, RF Applications EngineeringAmerican Technical Ceramics Corp.

RF to bebypassed

CO

LSCP

RS

Ω

Figure 1: BypassCapacitor Configuration

American Technical Ceramics • www.atceramics.com

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Excerpt from complete Circuit Designers’ Notebook, Document #001-927, Rev. E, 1/05